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<p><br/><b><span lang="EN-US" style="FONT-SIZE: 22pt; FONT-FAMILY: "Times New Roman","serif"; mso-font-kerning: 0pt;"> Lecture Notes on Optimization for<p></p></span></b></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><b><span lang="EN-US" style="FONT-SIZE: 22pt; FONT-FAMILY: "Times New Roman","serif"; mso-font-kerning: 0pt;">Microeconomic Analysis</span></b><b><span lang="EN-US" style="FONT-SIZE: 13pt; FONT-FAMILY: "Times New Roman","serif"; mso-font-kerning: 0pt;">1<p></p></span></b></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-size: 10.5pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">冯 曲<span lang="EN-US"><p></p></span></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-size: 10.5pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">复旦大学经济学院<span lang="EN-US"><p></p></span></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-size: 10.5pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">中国经济研究中心<span lang="EN-US"><p></p></span></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span style="FONT-SIZE: 15pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">第一稿 </span><span lang="EN-US" style="FONT-SIZE: 15pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman;">2003 </span><span style="FONT-SIZE: 15pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">年</span><span lang="EN-US" style="FONT-SIZE: 15pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman;">1 </span><span style="FONT-SIZE: 15pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">月<span lang="EN-US"><p></p></span></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-size: 10.5pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">一切匠心都归功于</span><span lang="EN-US" style="FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-size: 10.5pt; mso-bidi-font-family: TimesNewRoman;">Dixit, Chiang, Takayama </span><span style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-size: 10.5pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">等杰出的前辈；所有的错误、遗漏为编者所有。<span lang="EN-US"><p></p></span></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-size: 10.5pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">他是个顽皮的孩子，不肯就安分的待在身旁；我们要做的是，不能让他的玩耍脱离我<span lang="EN-US"><p></p></span></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span style="FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-bidi-font-size: 10.5pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">们的视线。<span lang="EN-US"><p></p></span></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="FONT-SIZE: 5.5pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman;">1 </span><span style="FONT-SIZE: 9pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: "Times New Roman"; mso-bidi-font-family: 宋体;">欢迎指出错误及评论。</span><span lang="EN-US" style="FONT-SIZE: 9pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman;"><a href="mailto:qufeng@fudan.edu.cn">qufeng@fudan.edu.cn</a><p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="FONT-SIZE: 9pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman;"><p> </p></span></p><p> </p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">目 录<span lang="EN-US"><p></p></span></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">A.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">最优规划问题</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………..………..3<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">B.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">梯度向量</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………………………3<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">B.1.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">无约束极值问题</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………..3<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">B.1.1 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">向量的内积</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………4<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">B.2.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">约束极值问题</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………………..6<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">B.2.1 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">雅克比矩阵</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………8<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">B.2.2 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">隐函数定理</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………8<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">B.2.3 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">超平面</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">………………………………………………………9<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">C.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">等式约束极值的拉格朗日求解法</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………..10<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">D.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">非线性规划问题的求解：库恩－塔克条件</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………..11<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">E.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">二阶条件</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">………………………………………………………………..14<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">E.1 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">无约束极值问题</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………14<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">E.1.1 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">泰勒展开</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………..14<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">E.1.2 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">二次型</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………….16<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">E.2 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">等式约束极值问题</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………….17<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">E.3 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">不等式约束问题</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">………………………………………………….21<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">F.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">凹规划</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………………………………22<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">F.1.1 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">凸集</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………………22<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">F.1.2 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">凸函数</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">………………………………………………………22<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">F.1.3.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">凹函数</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">………………………………………………………23<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">F.2.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">凹规划</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………………………..24<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">F.3.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">拟凹函数、拟凸函数</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………..25<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">最优化问题的解</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………………28<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.1.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">基本概念</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………………..28<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.1.1 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">紧集</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………………28<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.1.2.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">函数的连续</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………28<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.1.3 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">韦氏定理</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………………28<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.2.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">解的存在性和唯一性</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………..29<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.2.1.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">存在性定理</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………29<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.2.2 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">唯一性定理</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………30<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">G.3 </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">分离</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………………………….31<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">H.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">比较静态分析</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………………………33<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">H.1.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">基本思想 </span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………………33<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">H.2.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">一般方法</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………...……………………34<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">I. </span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">包络定理</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………….…………………….36<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">I.1.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">最大值函数</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">…………………………………………………………36<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">I.2.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">包络定理</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………………………37<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">I.3.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">拉格朗日乘子的含义</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">………………………………………………39<p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">I.4.</span><span style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-font-kerning: 0pt; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 宋体;">包络定理的应用</span><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: "TimesNewRoman","serif"; mso-font-kerning: 0pt; mso-bidi-font-family: TimesNewRoman; mso-fareast-font-family: 宋体;">……………………………………………………40</span></p><p></p>
[此贴子已经被作者于2007-11-28 13:19:50编辑过] |
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