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Convex Analysisの二,三の進展について

Preface 1. Decision-Theoretic Foundations 1.1 Game Theory, Rationality, and Intelligence 1.2 Basic Concepts of Decision Theory 1.3 Axioms 1.4 The Expected-Utility Maximization Theorem 1.5 Equivalent Representations 1.6 Bayesian Conditional-Probability Systems 1.7 Limitations of the Bayesian Model 1.8 Domination 1.9 Proofs of the Domination Theorems Exercises 2. Basic Models 2.1 Games in Extensive Form 2.2 Strategic Form and the Normal Representation 2.3 Equivalence of Strategic-Form Games 2.4 Reduced Normal Representations 2.5 Elimination of Dominated Strategies 2.6 Multiagent Representations 2.7 Common Knowledge 2.8 Bayesian Games 2.9 Modeling Games with Incomplete Information Exercises 3. Equilibria of Strategic-Form Games 3.1 Domination and Ratonalizability 3.2 Nash Equilibrium 3.3 Computing Nash Equilibria 3.4 Significance of Nash Equilibria 3.5 The Focal-Point Effect 3.6 The Decision-Analytic Approach to Games 3.7 Evolution. Resistance. and Risk Dominance 3.8 Two-Person Zero-Sum Games 3.9 Bayesian Equilibria 3.10 Purification of Randomized Strategies in Equilibria 3.11 Auctions 3.12 Proof of Existence of Equilibrium 3.13 Infinite Strategy Sets Exercises 4. Sequential Equilibria of Extensive-Form Games 4.1 Mixed Strategies and Behavioral Strategies 4.2 Equilibria in Behavioral Strategies 4.3 Sequential Rationality at Information States with Positive Probability 4.4 Consistent Beliefs and Sequential Rationality at All Information States 4.5 Computing Sequential Equilibria 4.6 Subgame-Perfect Equilibria 4.7 Games with Perfect Information 4.8 Adding Chance Events with Small Probability 4.9 Forward Induction 4.10 Voting and Binary Agendas 4.11 Technical Proofs Exercises 5. Refinements of Equilibrium in Strategic Form 5.1 Introduction 5.2 Perfect Equilibria 5.3 Existence of Perfect and Sequential Equilibria 5.4 Proper Equilibria 5.5 Persistent Equilibria 5.6 Stable Sets 01 Equilibria 5.7 Generic Properties 5.8 Conclusions Exercises 6. Games with Communication 6.1 Contracts and Correlated Strategies 6.2 Correlated Equilibria 6.3 Bayesian Games with Communication 6.4 Bayesian Collective-Choice Problems and Bayesian Bargaining Problems 6.5 Trading Problems with Linear Utility 6.6 General Participation Constraints for Bayesian Games with Contracts 6.7 Sender-Receiver Games 6.8 Acceptable and Predominant Correlated Equilibria 6.9 Communication in Extensive-Form and Multistage Games Exercises Bibliographic Note 7. Repeated Games 7.1 The Repeated Prisoners Dilemma 7.2 A General Model of Repeated Garnet 7.3 Stationary Equilibria of Repeated Games with Complete State Information and Discounting 7.4 Repeated Games with Standard Information: Examples 7.5 General Feasibility Theorems for Standard Repeated Games 7.6 Finitely Repeated Games and the Role of Initial Doubt 7.7 Imperfect Observability of Moves 7.8 Repeated Wines in Large Decentralized Groups 7.9 Repeated Games with Incomplete Information 7.10 Continuous Time 7.11 Evolutionary Simulation of Repeated Games Exercises 8. Bargaining and Cooperation in Two-Person Games 8.1 Noncooperative Foundations of Cooperative Game Theory 8.2 Two-Person Bargaining Problems and the Nash Bargaining Solution 8.3 Interpersonal Comparisons of Weighted Utility 8.4 Transferable Utility 8.5 Rational Threats 8.6 Other Bargaining Solutions 8.7 An Alternating-Offer Bargaining Game 8.8 An Alternating-Offer Game with Incomplete Information 8.9 A Discrete Alternating-Offer Game 8.10 Renegotiation Exercises 9. Coalitions in Cooperative Games 9.1 Introduction to Coalitional Analysis 9.2 Characteristic Functions with Transferable Utility 9.3 The Core 9.4 The Shapkey Value 9.5 Values with Cooperation Structures 9.6 Other Solution Concepts 9.7 Colational Games with Nontransferable Utility 9.8 Cores without Transferable Utility 9.9 Values without Transferable Utility Exercises Bibliographic Note 10. Cooperation under Uncertainty 10.1 Introduction 10.2 Concepts of Efficiency 10.3 An Example 10.4 Ex Post Inefficiency and Subsequent Oilers 10.5 Computing Incentive-Efficient Mechanisms 10.6 Inscrutability and Durability 10.7 Mechanism Selection by an Informed Principal 10.8 Neutral Bargaining Solutions 10.9 Dynamic Matching Processes with Incomplete Information Exercises Bibliography Index

博弈论 : 矛盾冲突分析 = Game theory : analysis of conflict

Computational geometry

Convex Analysis: (pms-28)

conditions and an accurate semidefinite programming solver," The Journal of the SDPA family for solving large-scale SDPs," in Handbook on Semidefinite. Semidefinite Programming, Combinatorial. Optimization and Primal semidefinite programming problem Handbook of Semidefinite Programming. Kluwer. Solving Euclidean distance matrix completion problems via semidefinite programming. AY Alfakih, A Khandani, H Wolkowicz. Computational optimization.

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Handbook of Semidefinite Programming

We survey duality theories for quasiconvex optimization problems, based on notions of generalized conjugation. Some of them are obtained from Moreau's generalized conjugation, while the others are special cases of the so-called H-duality. The relationship existing between the two kinds of approaches is described.

Quasiconvex duality theory by generalized conjugation methods

A theorem due to Fitzpatrick provides a representation of arbitrary maximal monotone operators by convex functions. This paper explores representability of arbitrary (nonnecessarily maximal) monotone operators by convex functions. In the finite-dimensional case, we identify the class of monotone operators that admit a convex representation as the one consisting of intersections of maximal monotone operators and characterize the monotone operators that have a unique maximal monotone extension.

Monotone operators representable by l.s.c. convex functions

Preface. Part I: Generalized Convexity. 1. Are Generalized Derivatives Useful for Generalized Convex Functions? J.-P. Penot. 2. Stochastic Programs with Chance Constraints: Generalized Convexity and Approximation Issues R.J.-B. Wets. 3. Error Bounds for Convex Inequality Systems A.S. Lewis, Jong-Shi Pang. 4. Applying Generalised Convexity Notions to Jets A. Eberhard, et al. 5. Quasiconvexity via Two Step Functions A.M. Rubinov, B.M. Glover. 6. On Limiting Frechet epsilon-Subdifferentials A. Jourani, M. Thera. 7. Convexity Space with Respect to a Given Set L. Blaga, L. Lupsa. 8. A Convexity Condition for the Nonexistence of Some Antiproximinal Sets in the Space of Integrable Functions A.-M. Precupanu. 9. Characterizations of rho-Convex Functions M. Castellani, M. Pappalardo. Part II: Generalized Monotonicity. 10. Characterizations of Generalized Convexity and Generalized Monotonicity, a Survey J.-P. Crouzeix. 11. Quasimonotonicity and Pseudomonotonicity in Variational Inequalities and Equilibrium Problems N. Hadjisavvas, S. Schaible. 12. On the Scalarization of Pseudoconcavity and Pseudomonotonicity Concepts for Vector Valued Functions R. Cambini, S. Komlosi. 13. Variational Inequalities and Pseudomonotone Functions: Some Characterizations R. John. Part III: Optimality Conditions and Duality. 14. Simplified Global Optimality Conditions in Generalized Conjugation Theory F. Flores-Bazan, J.-E. Martinez-Legaz. 15. Duality in DC Programming B. Lemaire, M.Volle. 16. Recent Developments in Second Order Necessary Optimality Conditions A. Cambini, et al. 17. Higher Order Invexity and Duality in Mathematical Programming B. Mond, J. Zhang. 18. Fenchel Duality in Generalized Fractional Programming C.R. Bector, et al. Part IV: Vector Optimization. 19. The Notion of Invexity in Vector Optimization: Smooth and Nonsmooth Case G. Giorgi, A. Guerraggio. 20. Quasiconcavity of Sets and Connectedness of the Efficient Frontier in Ordered Vector Spaces E. Molho, A. Zaffaroni. 21. Multiobjective Quadratic Problem: Characterization of the Efficient Points A. Beato-Moreno, et al. 22. Generalized Concavity for Bicriteria Functions R. Cambini. 23. Generalized Concavity in Multiobjective Programming A. Cambini, L. Martein.

Generalized Convexity, Generalized Monotonicity: Recent Results

This article presents an approach to generalized convex duality theory based on Fenchel-Moreau conjugations; in particular, it discusses quasiconvex conjugation and duality in detail. It also describes the related topic of microeconomics duality and analyzes the monotonicity of demand functions.

Juan Enrique Martínez-Legaz

Papers

Quasiconvex duality theory by generalized conjugation methods

Monotone operators representable by l.s.c. convex functions

Generalized Convexity, Generalized Monotonicity: Recent Results

Generalized Convex Duality and its Economic Applicatons

Duality in D.C. Programming: The Case of Several D.C. Constraints