Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
Minimax Theorems - MaRDI portal

Minimax Theorems

From MaRDI portal
Publication:5817580

DOI10.1073/pnas.39.1.42zbMath0050.06501OpenAlexW2578992305WikidataQ33713138 ScholiaQ33713138MaRDI QIDQ5817580

Ky Fan

Publication date: 1953

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.39.1.42




Related Items

Continuous-time zero-sum games for markov decision processes with discounted risk-sensitive cost criterion on a general state spaceMinimal indefinite Randomisierungen von SpielenDiscrete-time zero-sum Markov games with first passage criteriaA unified study of existence theorems in topologically based settings and applications in optimizationAn ε-equilibrium point in ann-person game with constraintsDominated Convergence and Stone-Weierstrass TheoremDistributionally robust portfolio optimization with linearized STARR performance measureMinimax inequalities inG-convex spacesOn duality for nonconvex minimization problems within the framework of abstract convexityThe minimum mean square estimator of integrable variables under sublinear operatorsZero-sum semi-Markov games with a probability criterionZero-sum infinite-horizon discounted piecewise deterministic Markov gamesThe application of a universal separating vector lemma to optimal sampled-data control problems with nonsmooth Mayer cost functionPreference robust distortion risk measure and its applicationPreference robust state-dependent distortion risk measure on act space and its application in optimal decision makingSystemic risk of optioned portfolio: controllability and optimizationZero-sum games involving teams against teams: existence of equilibria, and comparison and regularity in informationA martingale minimax exponential inequality for Markov chainsTikhonov regularization for a class of generalized hemivariational inequality in Banach spacesRobust matching for teamsConjugation-based approach to the \(\varepsilon\)-subdifferential of convex supremaSet valued equilibrium problems without linear structureUnnamed ItemOPTIMAL INSURANCE CONTRACTS UNDER DISTORTION RISK MEASURES WITH AMBIGUITY AVERSIONUnnamed ItemUnnamed ItemUnnamed ItemUnnamed ItemNonzero-sum games for continuous-time Markov chains with unbounded discounted payoffsZero-Sum Two Person GamesCausal transport plans and their Monge–Kantorovich problemsUnlocking of predicate: application to constructing a non-anticipating selectionUnnamed ItemA Convex and Exact Approach to Discrete Constrained TV-L1 Image ApproximationDynamic optimization for reachability problems.Minimax Results on Dense Sets and Dense Families of FunctionalsZero-sum games for continuous-time jump Markov processes in Polish spaces: discounted payoffsOn the existence of an efficient hedge for an American contingent claim within a discrete time marketOn weakly correlated and correlated equilibria in discontinuous gamesExistence conditions in general quasimonotone variational inequalitiesUnnamed ItemAlternative and minimax theorems beyond vector spaces.On the Generalized Duality Principle for State-Constrained Control and State Estimation Under Impulsive InputsOn Borel probability measures and noncooperative game theoryZero-Sum Stopping Games with Asymmetric InformationA Continuous Updating Rule for Imprecise ProbabilitiesOn some vector valued Markov gameDuality Results and Dual Bundle Methods Based on the Dual Method of Centers for Minimax Fractional ProgramsSubdifferential Formulae for the Supremum of an Arbitrary Family of FunctionsLe Her with s Suits and d DenominationsComparison of Information Structures for Zero-Sum Games and a Partial Converse to Blackwell Ordering in Standard Borel SpacesOn minimax theorems for lower semicontinuous functions in Hilbert spacesExtensions of the Cav(u) Theorem for Repeated Games with Incomplete Information on One SideTwo-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on maximum overlap using directional iteratesApproximation Theorems for Zero-Sum Nonstationary Stochastic GamesCommutative Stochastic GamesKalman--Bucy Filtering and Minimum Mean Square Estimator under UncertaintyUnnamed ItemUnnamed ItemContinuous-time zero-sum games for Markov chains with risk-sensitive finite-horizon cost criterionGeneralized hierarchical minimax theorems for set-valued mappingsSemicontinuous nonstationary stochastic gamesIntroduction to the symposium on discontinuous gamesRemarks on the existence and stability of some relaxed Nash equilibrium in strategic form gamesDual representations for systemic risk measures based on acceptance setsSome new generalizations of nonempty intersection theorems without convexity assumptions and essential stability of their solution set with applicationsImage convexity of generalized systems with infinite-dimensional image and applicationsOptimal stopping under model uncertainty: randomized stopping times approachAbstract Kuhn-Tucker theoremsA sharp Lagrange multiplier theorem for nonlinear programsZero-sum stochastic games with average payoffs: new optimality conditionsSome minimax problems of vector-valued functionsA note on König and close convexity in minimax theoremsA minimax theorem for vector-valued functionsZero-sum continuous-time Markov games with unbounded transition and discounted payoff ratesNonlinear programming via König's maximum theoremBest approximation in the space of continuous vector-valued functionsHomogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equationDiagonal convexity conditions for problems in convex analysis and quasi-variational inequalitiesOptimization techniques for state-constrained control and obstacle problemsExistence theorems for cone saddle points of vector-valued functions in infinite-dimensional spacesOn a D-solution of a cooperative m-person discounted Markov gameAn optimal variant of Kelley's cutting-plane methodPositive continuous linear functionals on Riesz spaces and applications to minimax theoremsNash equilibrium and minimax theorem with \(\mathcal C\)-concavityParallel approximation of min-max problemsGeneralized Motzkin theorems of the alternative and vector optimization problemsEquivalence of a Ky Fan type minimax theorem and a Gordan type alternative theoremOn a dynamic fractional gameNearly subconvexlike set-valued maps and vector optimization problemsTwo-person zero-sum stochastic games with semicontinuous payoffA lower error estimate for cubature formulasOn synthesizing impulse controls and the theory of fast controlsSystems of convex inequalities and their applicationsMinimaxtheoreme und das IntegraldarstellungsproblemThe minimax principle and random programsExistence theorems of an extension for generalized strong vector quasi-equilibrium problemsGlobal minimization for continuous multiphase partitioning problems using a dual approachGeneralized \(\mathcal C\)-concave conditions and their applicationsA more refined convexity idea for Nash equilibriaRobust consumption-investment problem on infinite horizonVariational relation problem without the KKM property with applicationsBias and overtaking equilibria for zero-sum stochastic differential gamesOn a minimax theorem of Terkelsen'sAn indistinguishability result on rationalizability under general preferencesNondifferentiable minimax fractional programming in complex spaces with parametric dualityA general solution concept for two-person, zero-sum gamesOn the existence of values for arbitration gamesDuality for set-valued multiobjective optimization problems. II: Optimal controlOn the problem of impulse measurement feedback controlExistence of the uniform value in zero-sum repeated games with a more informed controllerA prequential test for exchangeable theoriesRobust portfolio optimization with a generalized expected utility model under ambiguityMultivalued variational inequalities and coincidence point resultsComments on ``Dual methods for nonconvex spectrum optimization of multicarrier systemsEpsilon-net method for optimizations over separable statesHamiltonian systems as selfdual equationsMoreau-Rockafellar theorems for nonconvex set-valued mapsThe maximum theorem and the existence of Nash equilibrium of (generalized) games without lower semicontinuitiesCorrelated relaxed equilibria in nonzero-sum linear differential gamesElementary convex techniques for equilibrium, minimax and variational problemsSome minimax problems in lexicographic orderFinitely additive and measurable stochastic gamesA continuity theorem for Stinespring's dilationStochastic games with unbounded payoffs: applications to robust control in economicsData-based decisions under imprecise probability and least favorable modelsDuality on a nondifferentiable minimax fractional programmingMinimax results and finite-dimensional separationBipotentials for non-monotone multivalued operators: fundamental results and applicationsInfinite sequential games with perfect but incomplete informationOn a continuous solution to the Bellman-Poisson equation in stochastic gamesA minimax theorem for vector-valued functions in lexicographic orderApproximating saddle points as equilibria of differential inclusionsZero-sum risk-sensitive stochastic gamesExistence of Nash equilibria with \(\mathcal C\)-convexityThe problem of control for multi-agent motion: general relationsOn the problem of control for ellipsoidal motionsSemicontinuous nonstationary stochastic games. IIDirect and inverse addition in convex analysis and applicationsA nonmanipulable testBemerkungen zum von Neumannschen MinimaxtheoremGeneralized saddle points theorems for set-valued mappings in locally generalized convex spacesZero-sum ergodic semi-Markov games with weakly continuous transition probabilitiesExistence theorems and extreme solutions for inequalities concerning convex functions or linear transformationsMinimum distance estimation in imprecise probability modelsAn inexact primal-dual algorithm for semi-infinite programmingOn the use of KKM multifunctions in fixed point theory and related topicsExistence results and gap functions for the generalized equilibrium problem with composed functionsA noncooperative \(n\)-person semi-Markov game with a separable metric state spaceA generalization of a minimax theorem of Fan via a theorem of the alternativeMinimaximin results with applications to economic equilibriumInequality systems and minimax theoremsNote on my paper A simple proof for von Neumann's minimax theoremUniform approximation and a generalized minimax theoremInequality systems and minimax results without linear structureCriterion for complete determinacy for concave-convexlike gamesA generalization of the Arrow-Barankin-Blackwell theorem in normed spacesInequality systems and optimizationNonzero-sum stochastic differential games with additive structure and average payoffsMinimax selection theoremsA general min-max theoremConvexlike alternative theorems and mathematical programmingDiscontinuous implicit quasivariational inequalities in normed spacesExcesses, duality gaps and weak compactnessStronger maximal monotonicity properties of linear operatorsDorronsoro's theorem and a slight generalizationUnnamed ItemStrong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communicationOn Fan's minimax theoremUniformly quasiconvexlike functionsMinimax theorems without linear structureAn upward-downward minimax theoremIdempotent Expansions for Continuous-Time Stochastic Control\(L\)-topological meet theoremsThe minimax equality; sufficient and necessary conditionsSaddle points of discrete Markov zero-sum game with stoppingZero-sum continuous-time Markov pure jump game over a fixed durationA new minimax inequality on H-spaces with applicationsA saddlepoint theorem for set-valued mapsDimensions of random statistically self-affine Sierpinski sponges in \(\mathbb{R}^k\)An intersection theorem for topological vector spaces and applicationsStrong converse exponent for classical-quantum channel codingControl of ellipsoidal trajectories: Theory and numerical resultsSolvability theorems for classes of difference convex functionsTwo-person zero-sum stochastic games with varying discount factorsMinimax methods for open-loop equilibria in N-person differential games. Part I: Linear quadratic games and constrained gamesZero-sum games for continuous-time Markov jump processes with risk-sensitive finite-horizon cost criterionA note on maxmin problemA minimax approach for the study of systems of variational equations and related Galerkin schemesProximal bundle methods based on approximate subgradients for solving Lagrangian duals of minimax fractional programsA New Condition and Approach for Zero-Sum Stochastic Games with Average PayoffsRandomization is optimal in the robust principal-agent problemDuality for the $L^{\infty }$ optimal transport problemTopological Minimax TheoremsEstimation of high-dimensional change-points under a group sparsity structureDiscrete-time zero-sum games for Markov chains with risk-sensitive average cost criterionAugmented Lagrangian dual for nonconvex minimax fractional programs and proximal bundle algorithms for its resolutionGuaranteed deterministic approach to superhedging: mixed strategies and game equilibriumUnnamed ItemStrong vector equilibrium problemsOrbituary: ``Ky Fan (1914--2010), he spent every waking moment thinking about mathematicsDuality Formulas for Robust Pricing and Hedging in Discrete TimeExistence and asymptotic behaviour of positive ground state solution for critical Schrödinger-bopp-Podolsky systemA universal robust limit theorem for nonlinear Lévy processes under sublinear expectationApproachability, regret and calibration: implications and equivalencesSolving the complex quadratic double-ratio minimax optimization under a quadratic constraintThe Vanishing Discount Approach in a class of Zero-Sum Finite Games with Risk-Sensitive Average CriterionA note on the worst case approach for a market with a stochastic interest rateThe convex function determined by a multifunctionExact Bounds on the Truncated-Tilted Mean, with ApplicationsNon-convex infinite gamesAn ε-Minimax Theorem for Bi-Lower-Semicontinuous Set-Valued MappingsImage space approach and subdifferentials of integral functionalsClosed Convex Hulls of Unitary Orbits in von Neumann AlgebrasAsymptotics of the optimal value of the performance functional for a rapidly stabilizing indirect control in the regular caseThe dynamic programming method in impulsive control synthesisEllipsoidal methods for dynamics and control. ILagrangian duality and cone convexlike functionsSilent mixed duelsThe strong minimax theorem and strong saddle points of vector-valued functionsRecession maps and applicationsA general minimax theoremA note on limiting infisup theoremsRobust control and model misspecificationMinimax expected measure confidence sets for restricted location parametersReach set computation and control synthesis for discrete-time dynamical systems with disturbancesA new nonlinear scalarization function and applicationsMinimax theorems for Ф-convex functions: sufficient and necessary conditionsMerging and testing opinionsROBUST EXPONENTIAL HEDGING AND INDIFFERENCE VALUATIONVON NEUMANN, VILLE, AND THE MINIMAX THEOREMConditional nonlinear expectationsContinuous-time Markov games with asymmetric informationOn Fixed Point Theory and Its Applications to Equilibrium ModelsConvergence Analysis for Distributionally Robust Optimization and Equilibrium ProblemsMinimax theorems for set-valued maps without continuity assumptionsOptimal sequential and non-sequential procedures for evaluating a functionalZero-sum stochastic differential games with risk-sensitive costContinuous-time zero-sum games with probability criterionMinimax Theorem for Two Set-Valued Mappings with Nonconvex DomainsÜber das von-Neumannsche Minimax-TheoremQuantitative Stability Analysis for Distributionally Robust Optimization with Moment ConstraintsSome Nonclassical Problems in the Calculus of VariationsThe determinacy of infinite games with eventual perfect monitoringTheory and computational techniques for analysis of discrete-time control systems with disturbancesOn certain applications of the Hahn-Banach and minimax theoremsSolutions généralisées de certaines équations du type hypersurfaces minimaSum theorems for monotone operators and convex functionsPictures of monotone operatorsOn a generalized sup-inf problemFixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spacesSystems of linear inequalities on normed linear spacesLarge deviations for Markovian nonlinear Hawkes processesOperator Minimax Theorems in Banach LatticesOptimal matching problems with costs given by Finsler distancesOn the pointwise maximum of convex functionsA note on Ky Fan's minimax theoremDomain decomposition method for a model crack problem with a possible contact of crack edgesOn distributionally robust multiperiod stochastic optimizationAmbiguity, asset prices, and excess volatility in a pure-exchange economyTwo-function upward--downward minimax theoremsOn equivalent results in minimax theoryGeneralized KKM theorems, minimax inequalities, and their applicationsZero-sum discounted reward criterion games for piecewise deterministic Markov processesPotential analysis on Carnot groups. II: Relationship between Hausdorff measures and capacitiesRobust expected utility maximization with medial limitsAn optimal matching problem with constraintsMinimax theorems and cone saddle points of uniformly same-order vector- valued functionsGeneralized Arrow-Barankin-Blackwell theorems in locally convex spacesContinuous-time zero-sum games for Markov decision processes with discounted risk-sensitive cost criterionTopological minimax theorems and approximationExistence of solutions for lower semicontinuous quasi-equilibrium problemsSufficient optimality conditions and duality in vector optimization with invex-convexlike functionsInvex-convexlike functions and dualityTheorems of the alternative revisited and some extensions of Yuan's lemmaErrata corrige to: Stochastic differential games: Occupation measure based approachMinimax theorems with one-sided randomizationDiscontinuous implicit quasi-variational inequalities with applications to fuzzy mappingsExistence of solutions for mixed variational inequalities with perturbation in Banach spacesGeneral theorem on a finite support of mixed strategy in the theory of zero-sum gamesGeneralizations of a theorem of Arrow, Barankin, and Blackwell in topological vector spacesModel spaces for risk measuresA probability criterion for zero-sum stochastic gamesFull characterizations of minimax inequality, fixed point theorem, saddle point theorem, and KKM principle in arbitrary topological spacesRisk minimization, regret minimization and progressive hedging algorithmsOn the existence of solutions and Tikhonov regularization of hemivariational inequality problemsGeneralized minimax inequalities for set-valued mappingsCoefficients of ergodicity for Markov chains with uncertain parametersOptimal control of ellipsoidal motionsAmortized channel divergence for asymptotic quantum channel discriminationA generalized variational principle and its application to equilibrium problemsA minimax approach for inverse variational inequalitiesThe existence of Nash equilibrium in \(n\)-person games with \(\mathcal C\)-concavity.Geometry of the expected value set and the set-valued sample mean processExistence results for strong mixed vector equilibrium problem for multivalued mappingsEfficient hedging under ambiguity in continuous timeEfficient and weak efficient points in vector optimization with generalized cone convexityFormulae for the conjugate and the subdifferential of the supremum functionA minimax theorem for Lindelöf setsOptimality conditions and DC-Dinkelbach-type algorithm for generalized fractional programs with ratios of difference of convex functionsApproximation of discounted minimax Markov control problems and zero-sum Markov games using Hausdorff and Wasserstein distancesMinimax theorems for extended real-valued abstract convex-concave functionsOn \(\varepsilon\)-equilibrium point in a noncooperative \(n\)-person gameMinimax theorems with staircasesWeak finite intersection characterizations of existence in optimizationModules of families of vector measures on a Riemann surfaceWeighted \(L_ p\)-potential theory on homogeneous groupsGeneralizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarityRobust portfolio optimization with copulasGeneralized Knaster-Kuratowski-Mazurkiewicz theorem without convex hullAlmost monotone approximation in \(L_\infty\)Multilayer approach to minimax theoremsA note on the Ho-problem in Hilbert spaceRevisiting the Hahn-Banach theorem and nonlinear infinite programming\(p\)-module of vector measures in domains with intrinsic metric on Carnot groupsOn measurable minimax selectorsA minimax portfolio selection strategy with equilibriumA robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertaintyOn the optimal observation problemsNew generalized convexity notion for set-valued maps and application to vector optimizationDecomposition and discrete approximation methods for solving two-stage distributionally robust optimization problemsMulti-stage distributionally robust optimization with risk aversionDynamically consistent investment under model uncertainty: the robust forward criteriaMeasures as Lagrange multipliers in multistage stochastic programmingKolmogorov-type and general extension results for nonlinear expectationsOn interval portfolio selection problemVariational inequalities via the Hahn-Banach theoremTransfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterizationOn classes of generalized convex functions, Gordan-Farkas type theorems, and Lagrangean dualityA symmetric minimax theorem without linear structureDuality and regularization for inf-sup problemsZero duality gaps in infinite-dimensional programmingOptimal estimation and control of discrete multiplicative systems with unknown second-order statisticsMinimax theorems for interval spacesMinimax theorem and saddle point theorem without linear structureLagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued mapsOn an N-person noncooperative Markov game with a metric state spaceNew formulations of ambiguous volatility with an application to optimal dynamic contractingNumerical solution for an inverse variational problemThe least squares estimator of random variables under convex operators on \(L_{\mathcal{F}}^\infty (\mu)\) spaceOn convex generalized systemsThe random walk penalised by its range in dimensions \(d\geqslant 3\)Minimax type theorems for n-valued functionsThe Lagrangian, constraint qualifications and economicsInfinite zero-sum two-person gamesMinimax theorems for set-valued mappings.Doubles limites ordonnées et théorèmes de minimaxContinuity of equilibria for two-person zero-sum games with noncompact action sets and unbounded payoffsZero-sum semi-Markov games with state-action-dependent discount factorsAnalysis of the \(N\)-card version of the game Le HerA flexible minimax theoremA simple proof for König's minimax theoremA note on König's minimax theoremProper solutions of vector optimization problemsConvexlike and concavelike conditions in alternative, minimax, and minimization theoremsGeneral form of the Arrow-Barabkin-Blackwell theorem in normed spaces and the \(l^ \infty\)-caseCalculus for parabolic second-order derivativesExamples of max-flow and min-cut problems with duality gaps in continuous networksQuantitative stability analysis for minimax distributionally robust risk optimizationA Dini-Dax theorem