Holdings: Optima and equilibria

Optima and equilibria: an introduction to nonlinear analysis

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Bibliographic Details
Main Author:	Aubin, Jean-Pierre (Author)
Format:	Book
Language:	German English
Published:	Berlin [u.a.] Springer 2003
Edition:	2. ed., corr. 2. print.
Series:	Graduate texts in mathematics 140
Subjects:	Economics, Mathematical Mathematical analysis Nonlinear theories Optimierung Nichtlineare Analysis Spieltheorie Gleichgewichtstheorie Mathematisches Modell Gleichgewicht Einführung
Online Access:	Inhaltsverzeichnis
Item Description:	Aus d. Franz. übers.
Physical Description:	XVII, 433 S. graph. Darst.
ISBN:	3540649832

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MARC


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Record in the Search Index

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adam_text	TABLE OF CONTENTS PART I NONLINEAR ANALYSIS: THEORY 1 MINIMISATION PROBLEMS: GENERAL THEOREMS . . . . . . . . . . 9 1.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 EPIGRAPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 LOWER SECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 LOWER SEMI-CONTINUOUS FUNCTIONS . . . . . . . . . . . . . . . 11 1.6 LOWER SEMI-COMPACT FUNCTIONS . . . . . . . . . . . . . . . . 13 1.7 APPROXIMATE MINIMISATION OF LOWER SEMI-CONTINUOUS FUNC- TIONS ON A COMPLETE SPACE . . . . . . . . . . . . . . . . . . . 15 1.8 APPLICATION TO FIXED-POINT THEOREMS . . . . . . . . . . . . . 17 2 CONVEX FUNCTIONS AND PROXIMATION, PROJECTION AND SEPARA- TION THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 EXAMPLES OF CONVEX FUNCTIONS . . . . . . . . . . . . . . . . . 24 2.4 CONTINUOUS CONVEX FUNCTIONS . . . . . . . . . . . . . . . . . 25 2.5 THE PROXIMATION THEOREM . . . . . . . . . . . . . . . . . . . 27 2.6 SEPARATION THEOREMS . . . . . . . . . . . . . . . . . . . . . . 31 3 CONJUGATE FUNCTIONS AND CONVEX MINIMISATION PROBLEMS . 35 3.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 CHARACTERISATION OF CONVEX LOWER SEMI-CONTINUOUS FUNCTIONS 37 3.3 FENCHELS THEOREM . . . . . . . . . . . . . . . . . . . . . . . 39 3.4 PROPERTIES OF CONJ UGATE FUNCTIONS . . . . . . . . . . . . . . . 43 3.5 SUPPORT FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . 48 3.6 THE CRAM` ER TRANSFORM . . . . . . . . . . . . . . . . . . . . . 52 4 SUBDIFFERENTIALS OF CONVEX FUNCTIONS . . . . . . . . . . . . . . 57 4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.3 SUBDIFFERENTIABILITY OF CONVEX CONTINUOUS FUNCTIONS . . . . . 64 XII TABLE OF CONTENTS 4.4 SUBDIFFERENTIABILITY OF CONVEX LOWER SEMI-CONTINUOUS FUNC- TIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.5 SUBDIFFERENTIAL CALCULUS . . . . . . . . . . . . . . . . . . . . . 67 4.6 TANGENT AND NORMAL CONES . . . . . . . . . . . . . . . . . . . 70 5 MARGINAL PROPERTIES OF SOLUTIONS OF CONVEX MINIMISATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 FERMATS RULE . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.3 MINIMISATION PROBLEMS WITH CONSTRAINTS . . . . . . . . . . . 80 5.4 PRINCIPLE OF PRICE DECENTRALISATION . . . . . . . . . . . . . . . 82 5.5 REGULARISATION AND PENALISATION . . . . . . . . . . . . . . . . 84 6 GENERALISED GRADIENTS OF LOCALLY LIPSCHITZ FUNCTIONS . . . . 87 6.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.2 DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.3 ELEMENTARY PROPERTIES . . . . . . . . . . . . . . . . . . . . . 91 6.4 GENERALISED GRADIENTS . . . . . . . . . . . . . . . . . . . . . . 95 6.5 NORMAL AND TANGENT CONES TO A SUBSET . . . . . . . . . . . . 97 6.6 FERMATS RULE FOR MINIMISATION PROBLEMS WITH CONSTRAINTS . 99 7 TWO-PERSON GAMES. FUNDAMENTAL CONCEPTS AND EXAMPLES 101 7.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.2 DECISION RULES AND CONSISTENT PAIRS OF STRATEGIES . . . . . . 102 7.3 BROUWERS FIXED-POINT THEOREM (1910) . . . . . . . . . . . . 104 7.4 THE NEED TO CONVEXIFY: MIXED STRATEGIES . . . . . . . . . . . 105 7.5 GAMES IN NORMAL (STRATEGIC) FORM . . . . . . . . . . . . . . 106 7.6 PARETO OPTIMA . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.7 CONSERVATIVE STRATEGIES . . . . . . . . . . . . . . . . . . . . . 110 7.8 SOME FINITE GAMES . . . . . . . . . . . . . . . . . . . . . . . 112 7.9 COURNOTS DUOPOLY . . . . . . . . . . . . . . . . . . . . . . . 116 8 TWO-PERSON ZERO-SUM GAMES: THEOREMS OF VON NEUMANN AND KY FAN . . . . . . . . . . . . 125 8.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 8.2 VALUE AND SADDLE POINTS OF A GAME . . . . . . . . . . . . . . 125 8.3 EXISTENCE OF CONSERVATIVE STRATEGIES . . . . . . . . . . . . . . 130 8.4 CONTINUOUS PARTITIONS OF UNITY . . . . . . . . . . . . . . . . . 135 8.5 OPTIMAL DECISION RULES . . . . . . . . . . . . . . . . . . . . . 137 9 SOLUTION OF NONLINEAR EQUATIONS AND INCLUSIONS . . . . . . . . 143 9.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 9.2 UPPER HEMI-CONTINUOUS SET-VALUED MAPS . . . . . . . . . . . 144 9.3 THE DEBREUGALENIKA¨ DO THEOREM . . . . . . . . . . . . . . 148 9.4 THE TANGENTIAL CONDITION . . . . . . . . . . . . . . . . . . . 149 TABLE OF CONTENTS XIII 9.5 THE FUNDAMENTAL THEOREM FOR THE EXISTENCE OF ZEROS OF A SET-VALUED MAP . . . . . . . . . . . . . . . . . . . . . . . . . 150 9.6 THE VIABILITY THEOREM . . . . . . . . . . . . . . . . . . . . . 152 9.7 FIXED-POINT THEOREMS . . . . . . . . . . . . . . . . . . . . . . 154 9.8 EQUILIBRIUM OF A DYNAMICAL ECONOMY . . . . . . . . . . . . . 155 9.9 VARIATIONAL INEQUALITIES . . . . . . . . . . . . . . . . . . . . . 157 9.10 THE LERAYSCHAUDER THEOREM . . . . . . . . . . . . . . . . . 159 9.11 QUASI-VARIATIONAL INEQUALITIES . . . . . . . . . . . . . . . . . . 160 9.12 SHAPLEYS GENERALISATION OF THE THREE-POLES LEMMA . . . . . 162 10 INTRODUCTION TO THE THEORY OF ECONOMIC EQUILIBRIUM . . . . 167 10.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 10.2 EXCHANGE ECONOMIES . . . . . . . . . . . . . . . . . . . . . . 168 10.3 THE WALRASIAN MECHANISM . . . . . . . . . . . . . . . . . . . 169 10.4 ANOTHER MECHANISM FOR PRICE DECENTRALISATION . . . . . . . . 173 10.5 COLLECTIVE BUDGETARY RULE . . . . . . . . . . . . . . . . . . . 174 11 THE VON NEUMANN GROWTH MODEL . . . . . . . . . . . . . . . . 179 11.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 11.2 THE VON NEUMANN MODEL . . . . . . . . . . . . . . . . . . . 179 11.3 THE PERRONFROBENIUS THEOREM . . . . . . . . . . . . . . . . 184 11.4 SURJ ECTIVITY OF THE M MATRICES . . . . . . . . . . . . . . . . . 187 12 N -PERSON GAMES . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 12.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 12.2 NON-COOPERATIVE BEHAVIOUR . . . . . . . . . . . . . . . . . . . 189 12.3 N -PERSON GAMES IN NORMAL (STRATEGIC) FORM . . . . . . . . . 190 12.4 NON-COOPERATIVE GAMES WITH CONSTRAINTS (METAGAMES) . . . 192 12.5 PARETO OPTIMA . . . . . . . . . . . . . . . . . . . . . . . . . 193 12.6 BEHAVIOUR OF PLAYERS IN COALITIONS . . . . . . . . . . . . . . . 196 12.7 COOPERATIVE GAMES WITHOUT SIDE PAYMENTS . . . . . . . . . 197 12.8 EVOLUTIONARY GAMES . . . . . . . . . . . . . . . . . . . . . . 205 13 COOPERATIVE GAMES AND FUZZY GAMES . . . . . . . . . . . . . 211 13.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 13.2 COALITIONS, FUZZY COALITIONS AND GENERALISED COALITIONS OF N PLAYERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 13.3 ACTION GAMES AND EQUILIBRIUM COALITIONS . . . . . . . . . . 216 13.4 GAMES WITH SIDE PAYMENTS . . . . . . . . . . . . . . . . . . . 218 13.5 CORE AND SHAPLEY VALUE OF STANDARD GAMES . . . . . . . . . 226 XIV TABLE OF CONTENTS PART II NONLINEAR ANALYSIS: EXERCISES AND PROBLEMS 14 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 14.1 EXERCISES FOR CHAPTER 1 MINIMISATION PROBLEMS: GENERAL THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 14.2 EXERCISES FOR CHAPTER 2 * CONVEX FUNCTIONS AND PROXIMATION, PROJ ECTION AND SEPARATION THEOREMS . . . . . . . . . . . . . 242 14.3 EXERCISES FOR CHAPTER 3 * CONJUGATE FUNCTIONS AND CONVEX MINIMISATION PROBLEMS . . . . . . . . . . . . . . . . . . . . . 247 14.4 EXERCISES FOR CHAPTER 4 * SUBDIFFERENTIALS OF CONVEX FUNCTIONS 256 14.5 EXERCISES FOR CHAPTER 5 * MARGINAL PROPERTIES OF SOLUTIONS OF CONVEX MINIMISATION PROBLEMS . . . . . . . . . . . . . . . . 263 14.6 EXERCISES FOR CHAPTER 6 * GENERALISED GRADIENTS OF LOCALLY LIPSCHITZ FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . 270 14.7 EXERCISES FOR CHAPTER 8 * TWO-PERSON ZERO-SUM GAMES: THE- OREMS OF VON NEUMANN AND KY FAN . . . . . . . . . . . . . . 277 14.8 EXERCISES FOR CHAPTER 9 * SOLUTION OF NONLINEAR EQUATIONS AND INCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 14.9 EXERCISES FOR CHAPTER 10 * INTRODUCTION TO THE THEORY OF ECO- NOMIC EQUILIBRIUM . . . . . . . . . . . . . . . . . . . . . . . 287 14.10 EXERCISES FOR CHAPTER 11 * THE VON NEUMANN GROWTH MODEL 292 14.11 EXERCISES FOR CHAPTER 12 * N -PERSON GAMES . . . . . . . . . . 292 14.12 EXERCISES FOR CHAPTER 13 * COOPERATIVE GAMES AND FUZZY GAMES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 15 STATEMENTS OF PROBLEMS . . . . . . . . . . . . . . . . . . . . . . 303 15.1 PROBLEM 1 * SET-VALUED MAPS WITH A CLOSED GRAPH . . . . . 303 15.2 PROBLEM 2 * UPPER SEMI-CONTINUOUS SET-VALUED MAPS . . . . 303 15.3 PROBLEM 3 * IMAGE OF A SET-VALUED MAP . . . . . . . . . . . . 304 15.4 PROBLEM 4 * INVERSE IMAGE OF A SET-VALUED MAP . . . . . . . 304 15.5 PROBLEM 5 * POLARS OF A SET-VALUED MAP . . . . . . . . . . . . 305 15.6 PROBLEM 6 * MARGINAL FUNCTIONS . . . . . . . . . . . . . . . . 305 15.7 PROBLEM 7 * GENERIC CONTINUITY OF A SET-VALUED MAP WITH A CLOSED GRAPH . . . . . . . . . . . . . . . . . . . . . . . . . . 306 15.8 PROBLEM 8 * APPROXIMATE SELECTION OF AN UPPER SEMI-CONTINUOUS SET-VALUED MAP . . . . . . . . . . . . . . . . . . . . . . . . . 306 15.9 PROBLEM 9 * CONTINUOUS SELECTION OF A LOWER SEMI-CONTINUOUS SET-VALUED MAP . . . . . . . . . . . . . . . . . . . . . . . . . 307 15.10 PROBLEM 10 * INTERIOR OF THE IMAGE OF A CONVEX CLOSED CONE 307 15.11 PROBLEM 11 * DISCRETE DYNAMICAL SYSTEMS . . . . . . . . . . 310 15.12 PROBLEM 12 * FIXED POINTS OF CONTRACTIVE SET-VALUED MAPS . 312 15.13 PROBLEM 13 * APPROXIMATE VARIATIONAL PRINCIPLE . . . . . . . 313 15.14 PROBLEM 14 * OPEN IMAGE THEOREM . . . . . . . . . . . . . . 313 15.15 PROBLEM 15 * ASYMPTOTIC CENTRES . . . . . . . . . . . . . . . 315 15.16 PROBLEM 16 * FIXED POINTS OF NON-EXPANSIVE MAPPINGS . . . 316 TABLE OF CONTENTS XV 15.17 PROBLEM 17 * ORTHOGONAL PROJECTORS ONTO CONVEX CLOSED CONES 317 15.18 PROBLEM 18 * GAMMA-CONVEX FUNCTIONS . . . . . . . . . . . . 318 15.19 PROBLEM 19 * PROPER MAPPINGS . . . . . . . . . . . . . . . . 319 15.20 PROBLEM 20 * FENCHELS THEOREM FOR THE FUNCTIONS L ( X, AX ) 321 15.21 PROBLEM 21 CONJUGATE FUNCTIONS OF X * L ( X, AX ) . . . . . 322 15.22 PROBLEM 22 * HAMILTONIANS AND PARTIAL CONJUGATES . . . . . 323 15.23 PROBLEM 23 * LACK OF CONVEXITY AND FENCHELS THEOREM FOR PARETO OPTIMA . . . . . . . . . . . . . . . . . . . . . . . . . 324 15.24 PROBLEM 24 DUALITY IN LINEAR PROGRAMMING . . . . . . . . 325 15.25 PROBLEM 25 * LAGRANGIAN OF A CONVEX MINIMISATION PROBLEM 326 15.26 PROBLEM 26 * VARIATIONAL PRINCIPLES FOR CONVEX LAGRANGIANS 327 15.27 PROBLEM 27 * VARIATIONAL PRINCIPLES FOR CONVEX HAMILTONIANS 328 15.28 PROBLEM 28 * APPROXIMATION TO FERMATS RULE . . . . . . . . 329 15.29 PROBLEM 29 TRANSPOSES OF CONVEX PROCESSES . . . . . . . . 329 15.30 PROBLEM 30 * CONES WITH A COMPACT BASE . . . . . . . . . . 331 15.31 PROBLEM 31 * REGULARITY OF TANGENT CONES . . . . . . . . . . 331 15.32 PROBLEM 32 * TANGENT CONES TO AN INTERSECTION . . . . . . . 332 15.33 PROBLEM 33 * DERIVATIVES OF SET-VALUED MAPS WITH CONVEX GRAPHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 15.34 PROBLEM 34 * EPIDERIVATIVES OF CONVEX FUNCTIONS . . . . . . 334 15.35 PROBLEM 35 * SUBDIFFERENTIALS OF MARGINAL FUNCTIONS . . . . . 335 15.36 PROBLEM 36 * VALUES OF A GAME ASSOCIATED WITH A COVERING . 335 15.37 PROBLEM 37 * MINIMAX THEOREMS WITH WEAK COMPACTNESS ASSUMPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 15.38 PROBLEM 38 * MINIMAX THEOREMS FOR FINITE TOPOLOGIES . . . 337 15.39 PROBLEM 39 * KY FANS INEQUALITY . . . . . . . . . . . . . . . 338 15.40 PROBLEM 40 KY FANS INEQUALITY FOR MONOTONE FUNCTIONS . 339 15.41 PROBLEM 41 GENERALISATION OF THE GALENIKA¨DODEBREU THE- OREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 15.42 PROBLEM 42 EQUILIBRIUM OF COERCIVE SET-VALUED MAPS . . . 341 15.43 PROBLEM 43 * EIGENVECTORS OF SET-VALUED MAPS . . . . . . . . 341 15.44 PROBLEM 44 * POSITIVE EIGENVECTORS OF POSITIVE SET-VALUED MAPS 342 15.45 PROBLEM 45 * SOME VARIATIONAL PRINCIPLES . . . . . . . . . . . 343 15.46 PROBLEM 46 * GENERALISED VARIATIONAL INEQUALITIES . . . . . . 343 15.47 PROBLEM 47 * MONOTONE SET-VALUED MAPS . . . . . . . . . . . 345 15.48 PROBLEM 48 * WALRASIAN EQUILIBRIUM FOR SET-VALUED DEMAND MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 16 SOLUTIONS TO PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . 349 16.1 PROBLEM 1 * SOLUTION. SET-VALUED MAPS WITH A CLOSED GRAPH 349 16.2 PROBLEM 2 * SOLUTION. UPPER SEMI-CONTINUOUS SET-VALUED MAPS 349 16.3 PROBLEM 3 * SOLUTION. IMAGE OF A SET-VALUED MAP . . . . . . 350 16.4 PROBLEM 4 * SOLUTION. INVERSE IMAGE OF A SET-VALUED MAP . . 350 16.5 PROBLEM 5 * SOLUTION. POLARS OF A SET-VALUED MAP . . . . . . 352 16.6 PROBLEM 6 * SOLUTION. MARGINAL FUNCTIONS . . . . . . . . . . 352 XVI TABLE OF CONTENTS 16.7 PROBLEM 7 * SOLUTION. GENERIC CONTINUITY OF A SET-VALUED MAP WITH A CLOSED GRAPH . . . . . . . . . . . . . . . . . . . . . . 353 16.8 PROBLEM 8 * SOLUTION. APPROXIMATE SELECTION OF AN UPPER SEMI-CONTINUOUS SET-VALUED MAP . . . . . . . . . . . . . . . . 353 16.9 PROBLEM 9 * SOLUTION. CONTINUOUS SELECTION OF A LOWER SEMI- CONTINUOUS SET-VALUED MAP . . . . . . . . . . . . . . . . . . . 354 16.10 PROBLEM 10 * SOLUTION. INTERIOR OF THE IMAGE OF A CONVEX CLOSED CONE . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 16.11 PROBLEM 11 * SOLUTION. DISCRETE DYNAMICAL SYSTEMS . . . . . 358 16.12 PROBLEM 12 * SOLUTION. FIXED POINTS OF CONTRACTIVE SET-VALUED MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 16.13 PROBLEM 13 * SOLUTION. APPROXIMATE VARIATIONAL PRINCIPLE . 361 16.14 PROBLEM 14 * SOLUTION. OPEN IMAGE THEOREM . . . . . . . . 362 16.15 PROBLEM 15 * SOLUTION. ASYMPTOTIC CENTRES . . . . . . . . . . 364 16.16 PROBLEM 16 * SOLUTION. FIXED POINTS OF NON-EXPANSIVE MAP- PINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 16.17 PROBLEM 17 * SOLUTION. ORTHOGONAL PROJECTORS ONTO CONVEX CLOSED CONES . . . . . . . . . . . . . . . . . . . . . . . . . . 367 16.18 PROBLEM 18 * SOLUTION. GAMMA-CONVEX FUNCTIONS . . . . . . 368 16.19 PROBLEM 19 * SOLUTION. PROPER MAPPINGS . . . . . . . . . . . 369 16.20 PROBLEM 20 * SOLUTION. FENCHELS THEOREM FOR THE FUNCTIONS L ( X, AX ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 16.21 PROBLEM 21 SOLUTION. CONJUGATE FUNCTIONS OF X * L ( X, AX ) 371 16.22 PROBLEM 22 * SOLUTION. HAMILTONIANS AND PARTIAL CONJUGATES 371 16.23 PROBLEM 23 * SOLUTION. LACK OF CONVEXITY AND FENCHELS THE- OREM FOR PARETO OPTIMA . . . . . . . . . . . . . . . . . . . . 372 16.24 PROBLEM 24 SOLUTION. DUALITY IN LINEAR PROGRAMMING . . . 374 16.25 PROBLEM 25 * SOLUTION. LAGRANGIAN OF A CONVEX MINIMISATION PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 16.26 PROBLEM 26 * SOLUTION. VARIATIONAL PRINCIPLES FOR CONVEX LA- GRANGIANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 16.27 PROBLEM 27 * SOLUTION. VARIATIONAL PRINCIPLES FOR CONVEX HAMILTONIANS . . . . . . . . . . . . . . . . . . . . . . . . . . 376 16.28 PROBLEM 28 * SOLUTION. APPROXIMATION TO FERMATS RULE . . 377 16.29 PROBLEM 29 SOLUTION. TRANSPOSES OF CONVEX PROCESSES . . . 378 16.30 PROBLEM 30 * SOLUTION. CONES WITH A COMPACT BASE . . . . . 379 16.31 PROBLEM 31 * SOLUTION. REGULARITY OF TANGENT CONES . . . . . 380 16.32 PROBLEM 32 * SOLUTION. TANGENT CONES TO AN INTERSECTION . . 381 16.33 PROBLEM 33 * SOLUTION. DERIVATIVES OF SET-VALUED MAPS WITH CONVEX GRAPHS . . . . . . . . . . . . . . . . . . . . . . . . . 383 16.34 PROBLEM 34 * SOLUTION. EPIDERIVATIVES OF CONVEX FUNCTIONS . 384 16.35 PROBLEM 35 * SOLUTION. SUBDIFFERENTIALS OF MARGINAL FUNCTIONS 385 16.36 PROBLEM 36 * SOLUTION. VALUES OF A GAME ASSOCIATED WITH A COVERING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 TABLE OF CONTENTS XVII 16.37 PROBLEM 37 * SOLUTION. MINIMAX THEOREMS WITH WEAK COM- PACTNESS ASSUMPTIONS . . . . . . . . . . . . . . . . . . . . . . 387 16.38 PROBLEM 38 * SOLUTION. MINIMAX THEOREMS FOR FINITE TOPOLO- GIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 16.39 PROBLEM 39 * SOLUTION. KY FANS INEQUALITY . . . . . . . . . . 389 16.40 PROBLEM 40 SOLUTION. KY FANS INEQUALITY FOR MONOTONE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 16.41 PROBLEM 41 SOLUTION. GENERALISATIONS OF THE GALENIKA¨DO* DEBREU THEOREM . . . . . . . . . . . . . . . . . . . . . . . . 391 16.42 PROBLEM 42 * SOLUTION. EQUILIBRIUM OF COERCIVE SET-VALUED MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 16.43 PROBLEM 43 * SOLUTION. EIGENVECTORS OF SET-VALUED MAPS . . . 393 16.44 PROBLEM 44 * SOLUTION. POSITIVE EIGENVECTORS OF POSITIVE SET- VALUED MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 16.45 PROBLEM 45 * SOLUTION. SOME VARIATIONAL PRINCIPLES . . . . . 393 16.46 PROBLEM 46 * SOLUTION. GENERALISED VARIATIONAL INEQUALITIES . 395 16.47 PROBLEM 47 * SOLUTION. MONOTONE SET-VALUED MAPS . . . . . 397 16.48 PROBLEM 48 * SOLUTION. WALRASIAN EQUILIBRIUM FOR SET-VALUED DEMAND MAPS . . . . . . . . . . . . . . . . . . . . . . . . . . 399 APPENDIX 17 COMPENDIUM OF RESULTS . . . . . . . . . . . . . . . . . . . . . . 403 17.1 NONTRIVIAL, CONVEX, LOWER SEMI-CONTINUOUS FUNCTIONS . . . . 403 17.2 CONVEX FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . 405 17.3 CONJ UGATE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . 406 17.4 SEPARATION THEOREMS AND SUPPORT FUNCTIONS . . . . . . . . . 407 17.5 SUBDIFFERENTIABILITY . . . . . . . . . . . . . . . . . . . . . . . 410 17.6 TANGENT AND NORMAL CONES . . . . . . . . . . . . . . . . . . . 411 17.7 OPTIMISATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 17.8 TWO-PERSON GAMES . . . . . . . . . . . . . . . . . . . . . . . 415 17.9 SET-VALUED MAPS AND THE EXISTENCE OF ZEROS AND FIXED POINTS 417 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
any_adam_object	1
author	Aubin, Jean-Pierre
author_facet	Aubin, Jean-Pierre
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discipline	Mathematik
edition	2. ed., corr. 2. print.
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isbn	3540649832
language	German English
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spelling	Aubin, Jean-Pierre Verfasser aut L' analyse non linéaire et ses motivations économiques Optima and equilibria an introduction to nonlinear analysis Jean-Pierre Aubin 2. ed., corr. 2. print. Berlin [u.a.] Springer 2003 XVII, 433 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 140 Aus d. Franz. übers. Economics, Mathematical Mathematical analysis Nonlinear theories Optimierung (DE-588)4043664-0 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Spieltheorie (DE-588)4056243-8 gnd rswk-swf Gleichgewichtstheorie (DE-588)4071876-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Gleichgewicht (DE-588)4121372-5 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Spieltheorie (DE-588)4056243-8 s Gleichgewichtstheorie (DE-588)4071876-1 s Nichtlineare Analysis (DE-588)4177490-5 s DE-604 Gleichgewicht (DE-588)4121372-5 s Mathematisches Modell (DE-588)4114528-8 s Optimierung (DE-588)4043664-0 s Graduate texts in mathematics 140 (DE-604)BV000000067 140 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010507665&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Aubin, Jean-Pierre Optima and equilibria an introduction to nonlinear analysis Graduate texts in mathematics Economics, Mathematical Mathematical analysis Nonlinear theories Optimierung (DE-588)4043664-0 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Spieltheorie (DE-588)4056243-8 gnd Gleichgewichtstheorie (DE-588)4071876-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Gleichgewicht (DE-588)4121372-5 gnd
subject_GND	(DE-588)4043664-0 (DE-588)4177490-5 (DE-588)4056243-8 (DE-588)4071876-1 (DE-588)4114528-8 (DE-588)4121372-5 (DE-588)4151278-9
title	Optima and equilibria an introduction to nonlinear analysis
title_alt	L' analyse non linéaire et ses motivations économiques
title_auth	Optima and equilibria an introduction to nonlinear analysis
title_exact_search	Optima and equilibria an introduction to nonlinear analysis
title_full	Optima and equilibria an introduction to nonlinear analysis Jean-Pierre Aubin
title_fullStr	Optima and equilibria an introduction to nonlinear analysis Jean-Pierre Aubin
title_full_unstemmed	Optima and equilibria an introduction to nonlinear analysis Jean-Pierre Aubin
title_short	Optima and equilibria
title_sort	optima and equilibria an introduction to nonlinear analysis
title_sub	an introduction to nonlinear analysis
topic	Economics, Mathematical Mathematical analysis Nonlinear theories Optimierung (DE-588)4043664-0 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Spieltheorie (DE-588)4056243-8 gnd Gleichgewichtstheorie (DE-588)4071876-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Gleichgewicht (DE-588)4121372-5 gnd
topic_facet	Economics, Mathematical Mathematical analysis Nonlinear theories Optimierung Nichtlineare Analysis Spieltheorie Gleichgewichtstheorie Mathematisches Modell Gleichgewicht Einführung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010507665&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT aubinjeanpierre lanalysenonlineaireetsesmotivationseconomiques AT aubinjeanpierre optimaandequilibriaanintroductiontononlinearanalysis

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