发帖
雷达卡
Conjugate Duality in Economic Analysis.pdf
(7.59 MB, 需要: RMB 19 元)
2026最新的共轭对偶经济分析资料，500多页，内容丰富
全部矢量文字，方便翻译和投喂大模型。
Part I Optimization by Duality
1 Discovery and Proof Via Duality . 3
1.1 Euclidean Space . 5
1.2 Convex Function . 6
1.3 The Conjugate 7
1.4 Subdifferential 11
1.5 Perturbation Duality 13
References 17
2 No Duality Gap 19
2.1 Relative Condition . 20
2.2 Polyhedral Condition. 20
2.3 Reciprocal Dual . 21
Reference . 23
3 Fenchel Factors 25
3.1 Cost and Profit 25
3.2 Fenchel Duality . 29
Reference . 32
4 Conjugate Duality 33
4.1 Basic Separation . 34
4.2 Containing Closed Half-Space Representation . 35
4.3 Conjugate Duality 36
4.4 Concave Function 38
Reference . 38
5 Support 39
5.1 Supporting Hyperplane39
5.2 Geometric Interpretation of the Support . 40
5.3 Norm . 42
5.4 Partial Order 43
xxxvii
xxxviii Contents
5.5 Efficiency 44
5.6 Weak Efficiency . 45
5.7 Euclidean Jordan Algebra 47
References 48
6 Epigraph . 49
6.1 Support . 50
6.2 Epi-Multiplication . 50
6.3 Fenchel Equality . 51
6.4 Concave Function 53
References 54
7 Subdifferential . 55
7.1 Subgradient Inequality56
7.2 Subdifferential Calculus . 58
7.2.1 Subdifferential of a Sum 58
7.2.2 Partial Subdifferential 59
7.2.3 Envelope 61
References 63
8 Lagrangian . 65
8.1 Saddle Point 66
8.2 Karush-Kuhn-Tucker Example 68
8.3 Fenchel Duality . 70
8.4 Nonzero Perturbations71
8.5 Alternative Points-of-View . 72
Reference . 72
9 Karush-Kuhn-Tucker . 73
9.1 Primal 74
9.2 Lagrangian . 75
9.3 Dual 77
9.4 Exceptional Case 78
References 79
Part II Linear Algebra
10 Linear Transformation 83
10.1 Coordinate-Free . 83
10.2 Linear Transformation and Adjoint . 85
10.3 Extended Fenchel Duality 88
10.4 Moore-Penrose Generalized Inverse 90
10.5 Trace and Determinant91
References 92
11 Decomposition . 93
11.1 Spectral Decomposition . 93
11.2 Idempotent . 94
11.3 Singular-Value Decomposition 95
11.4 Trace and Determinant 97
12 Linear Equation . 99
12.1 Primal and Dual . 100
12.2 Value Function 101
Part III Economic Applications
13 Benefit and Cost . 105
13.1 Demand and Supply 106
13.2 Benefit and Cost Dual . 107
14 Diet . 111
References 114
15 Activity Analysis . 115
15.1 Weakly Efficient Production 116
15.2 Efficient Production 119
Reference . 121
16 Zero-Sum Game . 123
16.1 Nash Equilibrium 124
16.2 History 125
References 126
17 Assignment . 127
17.1 Doubly Stochastic Linear Transformations . 128
17.2 Assignment Primal and Dual 128
References 130
18 Constant Elasticity of Substitution . 131
18.1 Cost-Minimization . 131
18.2 Constant-Elasticity Function 133
18.3 Cobb–Douglas 135
18.4 Extremes 137
References 138
Part IV Cone Representation
19 Cone Representation of a Convex Set . 141
19.1 Cone Representation 141
19.2 Cone Generated by a Set . 145
19.3 Polar and Gauge . 146
References 148
20 Cone Representation of a Convex Function 149
20.1 Cone Representation of the Epigraph . 149
20.2 Cone Representation of the Conjugate . 150
xl Contents
20.3 Fenchel Equality for the Cone Representation . 151
20.4 Horizon Function 152
20.5 Polar Cones Generated by Contour Sets . 154
20.6 Horizon Cone of a Contour Set 155
20.7 Concave Function 156
Part V Local Analysis
21 Directional Derivative and Subdifferential . 159
Reference . 162
22 Normal Cone 163
22.1 Directional Derivative and Subdifferential 163
22.2 Contour Set 164
23 Subdifferential Calculus . 169
23.1 Sum 169
23.2 Composition with Linear Transformation 171
23.3 Chain Rule . 173
23.4 Finite Sum . 175
23.5 Maximum 177
24 Polyhedra 181
References 184
Part VI Euclidean Jordan Algebra
25 Euclidean Jordan Algebra . 187
25.1 Jordan, von Neumann, and Wigner . 188
25.2 Cone of Squares . 191
25.3 Direct Sum . 191
25.4 Classification . 192
References 193
26 Spectral Decomposition 195
26.1 Idempotents 196
26.2 Spectral Decomposition . 196
26.3 Trace Inner Product 199
26.4 Self-Adjoint Linear Transformations 203
26.5 Euclidean Jordan Algebra Direct Sum . 204
26.6 Isotope 204
References 205
27 Spectral Conjugate . 207
27.1 Simultaneous Ordered Spectral Decomposition 207
27.2 Trace Inequality . 208
27.3 Spectral Function 211
Contents xli
27.4 Application . 212
References 214
28 Quadratic Function . 215
28.1 Complementary Slackness . 215
28.2 Schur Complement . 216
28.3 Quadratic Function . 217
28.4 Fenchel Equality . 219
References 220
29 Lorentz Euclidean Jordan Algebra . 221
29.1 Jordan Product 222
29.2 Linear Representation . 223
29.3 Application . 224
References 225
30 Hermitian Euclidean Jordan Algebra . 227
30.1 Complexification 228
30.2 Hermitian Euclidean Jordan Algebra 229
30.3 Classification . 230
References 231
Part VII Mathematical Programming
31 Hahn–Banach . 235
31.1 Hahn–Banach Primal and Dual 236
31.2 Hahn–Banach Separation 236
31.3 Hahn–Banach Extension . 237
References 238
32 Ekeland Variational Principle . 239
References 242
33 Homogeneous Fractional Programming . 243
Reference . 247
34 Fractional Programming 249
34.1 Standard Fractional Program 250
34.2 Zero Conjugate 251
34.3 Homogeneous Fractional Program . 253
References 254
35 The Alternative 255
35.1 Cone Alternative . 256
35.2 Linear-Transformation Alternative . 257
35.3 Efficiency Alternative . 262
References 263
xlii Contents
Part VIII Efficiency
36 Efficiency Duality 267
36.1 Efficiency Duality 268
36.2 Weak-Efficiency Duality . 270
36.3 Activity Analysis 271
37 Weak Efficiency 273
37.1 Weak-Efficiency Primal and Dual 274
37.2 Exceptional Case 275
37.3 Value Maximization 276
38 Efficiency . 277
38.1 Efficiency Primal and Dual . 278
38.2 Exceptional Case 281
38.3 Arrow-Barankin-Blackwell . 281
References 283
Part IX Production
39 Domestic Product and Income 287
39.1 Production Equilibrium 288
39.2 Domestic-Product and Income Duality 288
References 290
40 Shephard Duality 291
40.1 Production and Cost 292
40.2 Four Equivalent Conditions . 294
40.3 Shephard Equality . 295
References 298
41 Heckscher-Ohlin Via Shephard Duality . 299
41.1 Domestic-Product Primal and Domestic-Income Dual . 300
41.2 Two Sectors and Two Inputs 302
41.3 Lerner Diagram . 304
References 305
42 Factor-Intensive Production Function 307
42.1 Factor-Intensive Production Function . 308
42.2 Factor-Price Frontier 309
42.3 Golden Rule of Saving 312
References 315
43 Heckscher-Ohlin Via Factor-Intensive Production Function . 317
43.1 Domestic-Product Primal 317
43.2 Domestic-Income Dual 319
43.3 Comparative Statics 321
References 325
Contents xliii
Part X Consumption
44 Hicks and Marshall Decompositions . 329
44.1 Expenditure Function and Indirect-Utility Function . 330
44.2 Axis Reversal . 332
References 338
45 Consumption Demand 339
45.1 Concave Utility 339
45.2 Classical Consumer 340
45.3 Directional Derivative and Subdifferential 341
45.4 Corner 342
45.5 Expenditure Minimization Versus Utility Maximization . 344
45.5.1 Expenditure Minimization . 344
45.5.2 Utility Maximization . 346
45.6 Examples 347
References 349
46 Indirect Utility . 351
46.1 Indirect Utility 351
46.2 Parallelogram Theorem 353
Reference . 356
47 Benefit . 357
47.1 Expenditure Function . 358
47.2 Benefit 358
47.3 Benefit Minus Cost Maximization 361
References 362
Part XI Welfare Economics
48 Resource Utilization 365
48.1 Exchange Economy 366
48.2 Resource Utilization 367
48.3 Coefficient of Resource Utilization . 369
48.4 Benefit 370
References 373
49 Welfare and Equilibrium 375
49.1 Exchange Economy 375
49.2 Weak Efficiency and Compensated Equilibrium . 376
49.3 Efficiency and Competitive Equilibrium . 378
Reference . 380
Part XII Core
50 Core and Equilibrium . 383
50.1 Exchange Economy 385
xliv Contents
50.2 Core of a Large Economy 386
50.3 The Weak Core and Compensated Equilibrium 387
50.4 The Core and Competitive Equilibrium 389
References 392
51 Bondareva-Shapley . 393
51.1 Cooperative Game . 393
51.2 Core 394
51.3 Core Primal and Dual . 395
References 396
Part XIII Econometrics
52 Moment Space . 399
52.1 Universal Space . 400
52.2 Cross-Moment Transformation 401
52.3 Coordinate-Free Versus Basis . 403
References 405
53 Least-Squares Linear Regression 407
53.1 Coefficient Least-Squares Linear Regression 408
53.2 Subspace Least-Squares Linear Regression . 409
53.3 Least-Squares Fractional Program 411
54 Multivariate Least-Squares Linear Regression . 415
54.1 Moment Space 415
54.2 Best Linear Regression 416
54.3 Reduced-Rank Least-Squares Linear Regression . 417
References 420
55 Instrumental Variables 421
55.1 Structural Equation . 422
55.2 Identification . 424
55.3 Analog Estimate . 426
55.4 Generalized Method of Moments 427
55.5 Two-Stage Least Squares 429
55.6 Statistical Inference 430
References 433
56 Likelihood Statistical Inference . 435
56.1 Wald Test 436
56.2 Constrained Maximum Likelihood . 437
56.3 Likelihood-Ratio Test . 438
56.4 Score Test 438
56.5 Lagrange-Multiplier Test 438
References 440
Contents xlv
57 Conjugate Maximum Likelihood 441
57.1 Comparative-Statics Variance . 442
57.2 Mean . 443
57.3 Variance . 444
Reference . 448
58 Maximum-Likelihood Estimation of Linear Regression 449
58.1 Concave Likelihood 449
58.2 Maximum Likelihood . 450
58.3 Conjugate Maximum Likelihood . 452
Part XIV Finance
59 Stochastic Discount Factor . 457
59.1 State Space and Asset Space 457
59.2 Stochastic Discount Factor . 458
59.3 Fundamental Theorem of Finance 459
59.4 Cost/Mean/Variance Efficient Portfolio 460
59.5 Pricing Payoff . 461
59.6 Cost and Mean Positivity 462
References 463
60 Expected Utility 465
60.1 von Neumann-Morgenstern Expected Utility 465
60.2 Budget Constraint 466
60.3 Expected-Utility Maximization 467
60.4 Constant Relative Risk Aversion . 469
60.5 Constant Absolute Risk Aversion 470
61 Price Bounds 473
61.1 Payoffs and Pricing . 473
61.2 Upper and Lower Price Bounds 474
61.3 Upper-Hedging Dual . 474
61.4 Two-State Example . 476
References 477
62 Sharpe Ratio 479
62.1 Sharpe Ratio 479
62.2 Hansen–Jagannathan Bound 482
References 485
63 Efficient-Portfolios Risk-Free Asset 487
63.1 Moment Space of Assets . 487
63.2 Excess Returns 488
63.3 Separation Theorem 489
References 491
xlvi Contents
64 Efficient Portfolios No Risk-Free Asset 493
64.1 Asset Space 493
64.2 Cost and Mean Positivity 494
64.3 Efficient Portfolios . 494
64.4 Minimum Variance . 496
65 Capital-Asset Pricing . 501
65.1 Asset Space 501
65.2 Mean/Variance Portfolio Choice . 502
65.3 Market Equilibrium 503
65.4 Efficient Risk Sharing . 504
References 508
66 Arbitrage Pricing Theory 509
66.1 Factor Model . 509
66.2 Moment Space of Portfolios 511
66.3 Systematic and No-Systematic Risk 512
66.4 Sharpe Ratio 513
66.5 Expected Excess Return . 515
References 516
Part XV Dynamics
67 Stability 519
67.1 Constant Coefficients, Linear Dynamic Systems . 520
67.2 Difference Equation 521
67.3 Differential Equation . 522
References 524
68 Balanced Growth 525
68.1 Balanced Growth .
. 526
68.2 Saddle Point 527
68.3 Nash Equilibrium 527
References 528
++++++++++++++++++++
【申报书范文】2024年省级市级教育教学成果奖申报书合集 https://bbs.pinggu.org/thread-12483283-1-1.html
【教学管理】课程思政教学案例资料合集 https://bbs.pinggu.org/thread-13165421-1-1.html
【学生竞赛资料】10000份挑战杯、互联网+、创新创业大赛资料合集（答辩模板、申请申报书） https://bbs.pinggu.org/thread-13029052-1-1.html
【教学管理】2024年更新-全国职业院校教学能力大赛资料合集（标准、方案、课件等） https://bbs.pinggu.org/thread-14742222-1-1.html
【课题项目申请申报】马列和D史D建-国家社科基金项目申请书标书范文 https://bbs.pinggu.org/thread-16671251-1-1.html
【课题项目申请申报】社会学、人口学与民族学-国家社科基金项目申请书范文 https://bbs.pinggu.org/thread-16671249-1-1.html
【课题项目申请申报】法学和政治学-国家社科基金项目申请书范文 https://bbs.pinggu.org/thread-16671245-1-1.html
【课题项目申请申报】管理学、教育学和艺术学-国家社科基金项目申请书范文 https://bbs.pinggu.org/thread-16671243-1-1.html
【课题项目申请申报】文学、历史学与哲学-国家社科基金项目申请书范文 https://bbs.pinggu.org/thread-16671240-1-1.html
【课题项目申请申报】经济学-国家社科基金项目申请书范文 https://bbs.pinggu.org/thread-16671238-1-1.html
【基金项目申请】国家社科、国家自科、教育部人文、教改、课程思政、一流本科课程资料 https://bbs.pinggu.org/thread-16315330-1-1.html
【课题申请资料】项目申请书、课题申报书研究框架图合集 https://bbs.pinggu.org/thread-16309537-1-1.html
【课题申报资料】课题项目申请书配套插图、框图、流程图、技术路线图合集 https://bbs.pinggu.org/thread-16308981-1-1.html
【课题基金】1050幅科研项目课题申报申报书插图合集（逻辑结构图、数据示意图、动画） https://bbs.pinggu.org/thread-16666695-1-1.html
【课题项目申请】2022—2025国家社科基金课题申请书范文 https://bbs.pinggu.org/thread-16620822-1-1.html
【课题项目基金】国家社科基金与教育部人文社科项目申请书申报书标书范文经验合集 https://bbs.pinggu.org/thread-16545433-1-1.html
【重磅课题资料】省中等职业教育教学改革项目课题资料汇总（申请书，开题，中期，结项 https://bbs.pinggu.org/thread-16437471-1-1.html
【教改课题】4份高等学校本科教学改革研究类课题项目申请书申报书 https://bbs.pinggu.org/thread-16437469-1-1.html
【职业学校与专业教育】双高计划申报材料、中期自评报告（院校，专业）超级合集 https://bbs.pinggu.org/thread-16608855-1-1.html
【科研绘图资料】课题项目申请申报书技术路线图与研究框架图合集（适用于各学科） https://bbs.pinggu.org/thread-16587826-1-1.html
【教师竞赛资料】教学创新大赛参考资料（青教赛、教创赛、教学能力比赛，赠国社科等） https://bbs.pinggu.org/thread-16586331-1-1.html
【教育教学管理】2025年最新省级市级校级高等教育教学成果奖申报书申报表合集 https://bbs.pinggu.org/thread-16578049-1-1.html
【课题项目】中小学高校教育课题申报立项资料材料模板报告结题材料 https://bbs.pinggu.org/thread-16339763-1-1.html
【课题申请资料】教学教改课题申报书教学能力实施报告模板多色架构图 https://bbs.pinggu.org/thread-16309678-1-1.html
2024年省市级教育教学成果奖合集 https://bbs.pinggu.org/thread-12483283-1-1.html
【科研课题】国家社科基金项目申报综合资料（2022-2005标书，开题，中期，结题等） https://bbs.pinggu.org/thread-14961969-1-1.html
【课题申请】2020—2005年国家自然科学基金中标标书申请书合集（管理学部）https://bbs.pinggu.org/thread-15032410-1-1.html
【基金申报】2022—2015年国家社科基金标书合集 https://bbs.pinggu.org/thread-11653799-1-1.html
【基金汇总】（2019—2005）国家社科基金申报资料（申请书、活页、中期检查、开题）等 https://bbs.pinggu.org/thread-11636754-1-1.html
【课题申请】国家社科基金与教育规划项目申请经验与范文合集 https://bbs.pinggu.org/thread-11494635-1-1.html
[学习资料] 【基金课题申报】管理学部、信息学部与数理学部-国家自然科学基金申请书标书合集 https://bbs.pinggu.org/thread-11346860-1-1.html
【基金申请】交叉学科的国家基金与教育部人文社科项目申报书合集 https://bbs.pinggu.org/thread-11564821-1-1.html
【教育教学管理】教学创新大赛超级资源包（青教赛、教创赛、教学能力比赛） https://bbs.pinggu.org/thread-15126291-1-1.html
【教育教学管理】2025职教宝库（教学能力大赛、教改课题、规划教材、教学成果奖） https://bbs.pinggu.org/thread-15036935-1-1.html
【课题申请】2020—2005年国家自然科学基金中标标书申请书合集（管理学部） https://bbs.pinggu.org/thread-15032410-1-1.html
【教育教学管理】本科高校省级立项申报书，课程思政，特等奖，教学成果奖，人才培养 https://bbs.pinggu.org/thread-14978398-1-1.html
【教育教学管理】2018-2024年国家、省教学成果奖超级资料包 https://bbs.pinggu.org/thread-14978393-1-1.html
【教育教学竞赛】教学创新大赛资料（青教赛、教创赛、教学能力比赛）赠送国社科申请 https://bbs.pinggu.org/thread-14978391-1-1.html
【科研课题】国家社科基金项目申报综合资料（2022-2005标书，开题，中期，结题等） https://bbs.pinggu.org/thread-14961969-1-1.html
【课题申请】历年国家社科基金申请书范例合集 https://bbs.pinggu.org/thread-11562407-1-1.html
https://bbs.pinggu.org/thread-8113337-1-1.html 【重要】国家社科基金申请书与论证活页
https://bbs.pinggu.org/thread-7980590-1-1.html 【基金申请资料】国家社科基金成功范例与经验学习资料
https://bbs.pinggu.org/thread-7855322-1-1.html 【基金申请】国家社科基金项目申请书范例与经验合集
【科研课题】省级教育规划项目申报材料、开题以及中期检查 https://bbs.pinggu.org/thread-11522095-1-1.html
https://bbs.pinggu.org/thread-10868549-1-1.html【重要】国家社科、教育部人文社科基金项目申报范文与经验
https://bbs.pinggu.org/thread-7979953-1-1.html 【重要】国家自然科学基金经管类成功范例
https://bbs.pinggu.org/thread-8019012-1-1.html 【基金申报资料】教育部人文社科基金项目申报书成功范例学习资料
https://bbs.pinggu.org/thread-8006896-1-1.html [学习资料] 教育部人文社科申报案例分析学习资料
https://bbs.pinggu.org/thread-7963726-11-1.html 【重点】教育部人文社科基金项目申请书范文
https://bbs.pinggu.org/thread-8748917-1-1.html [学习资料] 管理类国家自然科学基金申报书撰写学习资料
https://bbs.pinggu.org/thread-7967878-1-1.html [学习资料] 【基金申报资料】经管类国家自然科学基金申报范例学习资料
https://bbs.pinggu.org/thread-7967878-1-1.html 【基金申报资料】经管类国家自然科学基金申报范例学习资料
【课题申请】国家社科基金与教育规划项目申请经验与范文合集 https://bbs.pinggu.org/thread-11494635-1-1.html
【课题申报】国家重点研发计划项目申报书与答辩PPT范文 https://bbs.pinggu.org/thread-12468223-1-1.html
【营销管理】夜市、美食、集市、商业步行街、游园会活动策划方案合集 https://bbs.pinggu.org/thread-11840115-1-1.html
【旅游管理】2.4G智慧旅游与文旅小镇策划与规划方案合集 https://bbs.pinggu.org/thread-11836443-1-1.html
【商业管理】2020-2023最新三创赛与挑战杯案例资料合集（计划书策划书+PPT） https://bbs.pinggu.org/thread-11836424-1-1.html
【市场营销】2023年全国大学生市场调查与分析大赛资料 https://bbs.pinggu.org/thread-11834931-1-1.html
【商业管理】6200份商业计划书与项目策划书资料合集 https://bbs.pinggu.org/thread-11543286-1-1.html
【营销管理】800份互联网平台营销与广告案例资料（B站，小红书，抖音） https://bbs.pinggu.org/thread-11627149-1-1.html
[学习资料] 【营销管理】600份互联网营销方案案例合集 https://bbs.pinggu.org/thread-11627113-1-1.html
乡村振兴、田园综合体、乡村扶贫规划文本资料 https://bbs.pinggu.org/thread-11285862-1-1.html
[学习资料] 【三农管理】乡村振兴规划案例资料合集（2023年更新） https://bbs.pinggu.org/thread-11627052-1-1.html
2022年最新商业营销策划学习资料 https://bbs.pinggu.org/thread-10998743-1-1.html
【营销学习资料】商务活动策划与营销策划案例学习资料 https://bbs.pinggu.org/thread-10944060-1-1.html
医美营销策划资料 https://bbs.pinggu.org/thread-10889205-1-1.html
快消行业营销策划方案与案例学习资料 https://bbs.pinggu.org/thread-10871343-1-1.html
400份营销策划方案学习资料 https://bbs.pinggu.org/thread-10683076-1-1.html
餐饮、食品、休闲零食营销策划方案学习资料 https://bbs.pinggu.org/thread-11037931-1-1.html
1500份快消日用品营销案例 https://bbs.pinggu.org/thread-11042938-1-1.html
Excel审计底稿模板 https://bbs.pinggu.org/thread-10842624-1-1.html
会计师事务所审计底稿 https://bbs.pinggu.org/thread-10842619-1-1.html
内部审计底稿 https://bbs.pinggu.org/thread-10287768-1-1.html
会计文档与审计底稿资料 https://bbs.pinggu.org/thread-11044510-1-1.html
https://bbs.pinggu.org/thread-10429087-1-1.html 事务所审计工作实务学习资料
https://bbs.pinggu.org/thread-8252018-1-1.html 审计实务与工作底稿案例学习资料
https://bbs.pinggu.org/thread-11194304-1-1.html 审计报告常用模板与案例合集
https://bbs.pinggu.org/thread-10287768-1-1.html [学习资料] 内部审计底稿文档资料
https://bbs.pinggu.org/thread-10842619-1-1.html [学习资料] Excel版审计底稿模板学习资料
https://bbs.pinggu.org/thread-10842624-1-1.html [学习资料] 会计师事务所审计底稿学习资料
https://bbs.pinggu.org/thread-11073706-1-1.html 内部审计底稿与经验案例学习资料
https://bbs.pinggu.org/thread-11306657-1-1.html 【学习范例】审计底稿范例学习资料（word和Excel）合集
https://bbs.pinggu.org/thread-11246005-1-1.html 【管理资料】审计工作底稿、内部控制制度与手册、会计审核指导资料
https://bbs.pinggu.org/thread-11269243-1-1.html [学习资料] 审计底稿实例合集学习资料（2.1G）
https://bbs.pinggu.org/thread-11269243-1-1.html [学习资料] 财务管理、会计行业学习资料与工具模板合集
https://bbs.pinggu.org/thread-11306657-1-1.html 【实例资料】审计底稿实例学习资料（1.12G）
京公网安备 11010802022788号
