Minimax Theorems
From MaRDI portal
Publication:5817580
DOI10.1073/pnas.39.1.42zbMath0050.06501OpenAlexW2578992305WikidataQ33713138 ScholiaQ33713138MaRDI QIDQ5817580
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 space ⋮ Minimal indefinite Randomisierungen von Spielen ⋮ Discrete-time zero-sum Markov games with first passage criteria ⋮ A unified study of existence theorems in topologically based settings and applications in optimization ⋮ An ε-equilibrium point in ann-person game with constraints ⋮ Dominated Convergence and Stone-Weierstrass Theorem ⋮ Distributionally robust portfolio optimization with linearized STARR performance measure ⋮ Minimax inequalities inG-convex spaces ⋮ On duality for nonconvex minimization problems within the framework of abstract convexity ⋮ The minimum mean square estimator of integrable variables under sublinear operators ⋮ Zero-sum semi-Markov games with a probability criterion ⋮ Zero-sum infinite-horizon discounted piecewise deterministic Markov games ⋮ The application of a universal separating vector lemma to optimal sampled-data control problems with nonsmooth Mayer cost function ⋮ Preference robust distortion risk measure and its application ⋮ Preference robust state-dependent distortion risk measure on act space and its application in optimal decision making ⋮ Systemic risk of optioned portfolio: controllability and optimization ⋮ Zero-sum games involving teams against teams: existence of equilibria, and comparison and regularity in information ⋮ A martingale minimax exponential inequality for Markov chains ⋮ Tikhonov regularization for a class of generalized hemivariational inequality in Banach spaces ⋮ Robust matching for teams ⋮ Conjugation-based approach to the \(\varepsilon\)-subdifferential of convex suprema ⋮ Set valued equilibrium problems without linear structure ⋮ Unnamed Item ⋮ OPTIMAL INSURANCE CONTRACTS UNDER DISTORTION RISK MEASURES WITH AMBIGUITY AVERSION ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Nonzero-sum games for continuous-time Markov chains with unbounded discounted payoffs ⋮ Zero-Sum Two Person Games ⋮ Causal transport plans and their Monge–Kantorovich problems ⋮ Unlocking of predicate: application to constructing a non-anticipating selection ⋮ Unnamed Item ⋮ A Convex and Exact Approach to Discrete Constrained TV-L1 Image Approximation ⋮ Dynamic optimization for reachability problems. ⋮ Minimax Results on Dense Sets and Dense Families of Functionals ⋮ Zero-sum games for continuous-time jump Markov processes in Polish spaces: discounted payoffs ⋮ On the existence of an efficient hedge for an American contingent claim within a discrete time market ⋮ On weakly correlated and correlated equilibria in discontinuous games ⋮ Existence conditions in general quasimonotone variational inequalities ⋮ Unnamed Item ⋮ Alternative and minimax theorems beyond vector spaces. ⋮ On the Generalized Duality Principle for State-Constrained Control and State Estimation Under Impulsive Inputs ⋮ On Borel probability measures and noncooperative game theory ⋮ Zero-Sum Stopping Games with Asymmetric Information ⋮ A Continuous Updating Rule for Imprecise Probabilities ⋮ On some vector valued Markov game ⋮ Duality Results and Dual Bundle Methods Based on the Dual Method of Centers for Minimax Fractional Programs ⋮ Subdifferential Formulae for the Supremum of an Arbitrary Family of Functions ⋮ Le Her with s Suits and d Denominations ⋮ Comparison of Information Structures for Zero-Sum Games and a Partial Converse to Blackwell Ordering in Standard Borel Spaces ⋮ On minimax theorems for lower semicontinuous functions in Hilbert spaces ⋮ Extensions of the Cav(u) Theorem for Repeated Games with Incomplete Information on One Side ⋮ Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on maximum overlap using directional iterates ⋮ Approximation Theorems for Zero-Sum Nonstationary Stochastic Games ⋮ Commutative Stochastic Games ⋮ Kalman--Bucy Filtering and Minimum Mean Square Estimator under Uncertainty ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Continuous-time zero-sum games for Markov chains with risk-sensitive finite-horizon cost criterion ⋮ Generalized hierarchical minimax theorems for set-valued mappings ⋮ Semicontinuous nonstationary stochastic games ⋮ Introduction to the symposium on discontinuous games ⋮ Remarks on the existence and stability of some relaxed Nash equilibrium in strategic form games ⋮ Dual representations for systemic risk measures based on acceptance sets ⋮ Some new generalizations of nonempty intersection theorems without convexity assumptions and essential stability of their solution set with applications ⋮ Image convexity of generalized systems with infinite-dimensional image and applications ⋮ Optimal stopping under model uncertainty: randomized stopping times approach ⋮ Abstract Kuhn-Tucker theorems ⋮ A sharp Lagrange multiplier theorem for nonlinear programs ⋮ Zero-sum stochastic games with average payoffs: new optimality conditions ⋮ Some minimax problems of vector-valued functions ⋮ A note on König and close convexity in minimax theorems ⋮ A minimax theorem for vector-valued functions ⋮ Zero-sum continuous-time Markov games with unbounded transition and discounted payoff rates ⋮ Nonlinear programming via König's maximum theorem ⋮ Best approximation in the space of continuous vector-valued functions ⋮ Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation ⋮ Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities ⋮ Optimization techniques for state-constrained control and obstacle problems ⋮ Existence theorems for cone saddle points of vector-valued functions in infinite-dimensional spaces ⋮ On a D-solution of a cooperative m-person discounted Markov game ⋮ An optimal variant of Kelley's cutting-plane method ⋮ Positive continuous linear functionals on Riesz spaces and applications to minimax theorems ⋮ Nash equilibrium and minimax theorem with \(\mathcal C\)-concavity ⋮ Parallel approximation of min-max problems ⋮ Generalized Motzkin theorems of the alternative and vector optimization problems ⋮ Equivalence of a Ky Fan type minimax theorem and a Gordan type alternative theorem ⋮ On a dynamic fractional game ⋮ Nearly subconvexlike set-valued maps and vector optimization problems ⋮ Two-person zero-sum stochastic games with semicontinuous payoff ⋮ A lower error estimate for cubature formulas ⋮ On synthesizing impulse controls and the theory of fast controls ⋮ Systems of convex inequalities and their applications ⋮ Minimaxtheoreme und das Integraldarstellungsproblem ⋮ The minimax principle and random programs ⋮ Existence theorems of an extension for generalized strong vector quasi-equilibrium problems ⋮ Global minimization for continuous multiphase partitioning problems using a dual approach ⋮ Generalized \(\mathcal C\)-concave conditions and their applications ⋮ A more refined convexity idea for Nash equilibria ⋮ Robust consumption-investment problem on infinite horizon ⋮ Variational relation problem without the KKM property with applications ⋮ Bias and overtaking equilibria for zero-sum stochastic differential games ⋮ On a minimax theorem of Terkelsen's ⋮ An indistinguishability result on rationalizability under general preferences ⋮ Nondifferentiable minimax fractional programming in complex spaces with parametric duality ⋮ A general solution concept for two-person, zero-sum games ⋮ On the existence of values for arbitration games ⋮ Duality for set-valued multiobjective optimization problems. II: Optimal control ⋮ On the problem of impulse measurement feedback control ⋮ Existence of the uniform value in zero-sum repeated games with a more informed controller ⋮ A prequential test for exchangeable theories ⋮ Robust portfolio optimization with a generalized expected utility model under ambiguity ⋮ Multivalued variational inequalities and coincidence point results ⋮ Comments on ``Dual methods for nonconvex spectrum optimization of multicarrier systems ⋮ Epsilon-net method for optimizations over separable states ⋮ Hamiltonian systems as selfdual equations ⋮ Moreau-Rockafellar theorems for nonconvex set-valued maps ⋮ The maximum theorem and the existence of Nash equilibrium of (generalized) games without lower semicontinuities ⋮ Correlated relaxed equilibria in nonzero-sum linear differential games ⋮ Elementary convex techniques for equilibrium, minimax and variational problems ⋮ Some minimax problems in lexicographic order ⋮ Finitely additive and measurable stochastic games ⋮ A continuity theorem for Stinespring's dilation ⋮ Stochastic games with unbounded payoffs: applications to robust control in economics ⋮ Data-based decisions under imprecise probability and least favorable models ⋮ Duality on a nondifferentiable minimax fractional programming ⋮ Minimax results and finite-dimensional separation ⋮ Bipotentials for non-monotone multivalued operators: fundamental results and applications ⋮ Infinite sequential games with perfect but incomplete information ⋮ On a continuous solution to the Bellman-Poisson equation in stochastic games ⋮ A minimax theorem for vector-valued functions in lexicographic order ⋮ Approximating saddle points as equilibria of differential inclusions ⋮ Zero-sum risk-sensitive stochastic games ⋮ Existence of Nash equilibria with \(\mathcal C\)-convexity ⋮ The problem of control for multi-agent motion: general relations ⋮ On the problem of control for ellipsoidal motions ⋮ Semicontinuous nonstationary stochastic games. II ⋮ Direct and inverse addition in convex analysis and applications ⋮ A nonmanipulable test ⋮ Bemerkungen zum von Neumannschen Minimaxtheorem ⋮ Generalized saddle points theorems for set-valued mappings in locally generalized convex spaces ⋮ Zero-sum ergodic semi-Markov games with weakly continuous transition probabilities ⋮ Existence theorems and extreme solutions for inequalities concerning convex functions or linear transformations ⋮ Minimum distance estimation in imprecise probability models ⋮ An inexact primal-dual algorithm for semi-infinite programming ⋮ On the use of KKM multifunctions in fixed point theory and related topics ⋮ Existence results and gap functions for the generalized equilibrium problem with composed functions ⋮ A noncooperative \(n\)-person semi-Markov game with a separable metric state space ⋮ A generalization of a minimax theorem of Fan via a theorem of the alternative ⋮ Minimaximin results with applications to economic equilibrium ⋮ Inequality systems and minimax theorems ⋮ Note on my paper A simple proof for von Neumann's minimax theorem ⋮ Uniform approximation and a generalized minimax theorem ⋮ Inequality systems and minimax results without linear structure ⋮ Criterion for complete determinacy for concave-convexlike games ⋮ A generalization of the Arrow-Barankin-Blackwell theorem in normed spaces ⋮ Inequality systems and optimization ⋮ Nonzero-sum stochastic differential games with additive structure and average payoffs ⋮ Minimax selection theorems ⋮ A general min-max theorem ⋮ Convexlike alternative theorems and mathematical programming ⋮ Discontinuous implicit quasivariational inequalities in normed spaces ⋮ Excesses, duality gaps and weak compactness ⋮ Stronger maximal monotonicity properties of linear operators ⋮ Dorronsoro's theorem and a slight generalization ⋮ Unnamed Item ⋮ Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication ⋮ On Fan's minimax theorem ⋮ Uniformly quasiconvexlike functions ⋮ Minimax theorems without linear structure ⋮ An upward-downward minimax theorem ⋮ Idempotent Expansions for Continuous-Time Stochastic Control ⋮ \(L\)-topological meet theorems ⋮ The minimax equality; sufficient and necessary conditions ⋮ Saddle points of discrete Markov zero-sum game with stopping ⋮ Zero-sum continuous-time Markov pure jump game over a fixed duration ⋮ A new minimax inequality on H-spaces with applications ⋮ A saddlepoint theorem for set-valued maps ⋮ Dimensions of random statistically self-affine Sierpinski sponges in \(\mathbb{R}^k\) ⋮ An intersection theorem for topological vector spaces and applications ⋮ Strong converse exponent for classical-quantum channel coding ⋮ Control of ellipsoidal trajectories: Theory and numerical results ⋮ Solvability theorems for classes of difference convex functions ⋮ Two-person zero-sum stochastic games with varying discount factors ⋮ Minimax methods for open-loop equilibria in N-person differential games. Part I: Linear quadratic games and constrained games ⋮ Zero-sum games for continuous-time Markov jump processes with risk-sensitive finite-horizon cost criterion ⋮ A note on maxmin problem ⋮ A minimax approach for the study of systems of variational equations and related Galerkin schemes ⋮ Proximal bundle methods based on approximate subgradients for solving Lagrangian duals of minimax fractional programs ⋮ A New Condition and Approach for Zero-Sum Stochastic Games with Average Payoffs ⋮ Randomization is optimal in the robust principal-agent problem ⋮ Duality for the $L^{\infty }$ optimal transport problem ⋮ Topological Minimax Theorems ⋮ Estimation of high-dimensional change-points under a group sparsity structure ⋮ Discrete-time zero-sum games for Markov chains with risk-sensitive average cost criterion ⋮ Augmented Lagrangian dual for nonconvex minimax fractional programs and proximal bundle algorithms for its resolution ⋮ Guaranteed deterministic approach to superhedging: mixed strategies and game equilibrium ⋮ Unnamed Item ⋮ Strong vector equilibrium problems ⋮ Orbituary: ``Ky Fan (1914--2010), he spent every waking moment thinking about mathematics ⋮ Duality Formulas for Robust Pricing and Hedging in Discrete Time ⋮ Existence and asymptotic behaviour of positive ground state solution for critical Schrödinger-bopp-Podolsky system ⋮ A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation ⋮ Approachability, regret and calibration: implications and equivalences ⋮ Solving the complex quadratic double-ratio minimax optimization under a quadratic constraint ⋮ The Vanishing Discount Approach in a class of Zero-Sum Finite Games with Risk-Sensitive Average Criterion ⋮ A note on the worst case approach for a market with a stochastic interest rate ⋮ The convex function determined by a multifunction ⋮ Exact Bounds on the Truncated-Tilted Mean, with Applications ⋮ Non-convex infinite games ⋮ An ε-Minimax Theorem for Bi-Lower-Semicontinuous Set-Valued Mappings ⋮ Image space approach and subdifferentials of integral functionals ⋮ Closed Convex Hulls of Unitary Orbits in von Neumann Algebras ⋮ Asymptotics of the optimal value of the performance functional for a rapidly stabilizing indirect control in the regular case ⋮ The dynamic programming method in impulsive control synthesis ⋮ Ellipsoidal methods for dynamics and control. I ⋮ Lagrangian duality and cone convexlike functions ⋮ Silent mixed duels ⋮ The strong minimax theorem and strong saddle points of vector-valued functions ⋮ Recession maps and applications ⋮ A general minimax theorem ⋮ A note on limiting infisup theorems ⋮ Robust control and model misspecification ⋮ Minimax expected measure confidence sets for restricted location parameters ⋮ Reach set computation and control synthesis for discrete-time dynamical systems with disturbances ⋮ A new nonlinear scalarization function and applications ⋮ Minimax theorems for Ф-convex functions: sufficient and necessary conditions ⋮ Merging and testing opinions ⋮ ROBUST EXPONENTIAL HEDGING AND INDIFFERENCE VALUATION ⋮ VON NEUMANN, VILLE, AND THE MINIMAX THEOREM ⋮ Conditional nonlinear expectations ⋮ Continuous-time Markov games with asymmetric information ⋮ On Fixed Point Theory and Its Applications to Equilibrium Models ⋮ Convergence Analysis for Distributionally Robust Optimization and Equilibrium Problems ⋮ Minimax theorems for set-valued maps without continuity assumptions ⋮ Optimal sequential and non-sequential procedures for evaluating a functional ⋮ Zero-sum stochastic differential games with risk-sensitive cost ⋮ Continuous-time zero-sum games with probability criterion ⋮ Minimax Theorem for Two Set-Valued Mappings with Nonconvex Domains ⋮ Über das von-Neumannsche Minimax-Theorem ⋮ Quantitative Stability Analysis for Distributionally Robust Optimization with Moment Constraints ⋮ Some Nonclassical Problems in the Calculus of Variations ⋮ The determinacy of infinite games with eventual perfect monitoring ⋮ Theory and computational techniques for analysis of discrete-time control systems with disturbances ⋮ On certain applications of the Hahn-Banach and minimax theorems ⋮ Solutions généralisées de certaines équations du type hypersurfaces minima ⋮ Sum theorems for monotone operators and convex functions ⋮ Pictures of monotone operators ⋮ On a generalized sup-inf problem ⋮ Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces ⋮ Systems of linear inequalities on normed linear spaces ⋮ Large deviations for Markovian nonlinear Hawkes processes ⋮ Operator Minimax Theorems in Banach Lattices ⋮ Optimal matching problems with costs given by Finsler distances ⋮ On the pointwise maximum of convex functions ⋮ A note on Ky Fan's minimax theorem ⋮ Domain decomposition method for a model crack problem with a possible contact of crack edges ⋮ On distributionally robust multiperiod stochastic optimization ⋮ Ambiguity, asset prices, and excess volatility in a pure-exchange economy ⋮ Two-function upward--downward minimax theorems ⋮ On equivalent results in minimax theory ⋮ Generalized KKM theorems, minimax inequalities, and their applications ⋮ Zero-sum discounted reward criterion games for piecewise deterministic Markov processes ⋮ Potential analysis on Carnot groups. II: Relationship between Hausdorff measures and capacities ⋮ Robust expected utility maximization with medial limits ⋮ An optimal matching problem with constraints ⋮ Minimax theorems and cone saddle points of uniformly same-order vector- valued functions ⋮ Generalized Arrow-Barankin-Blackwell theorems in locally convex spaces ⋮ Continuous-time zero-sum games for Markov decision processes with discounted risk-sensitive cost criterion ⋮ Topological minimax theorems and approximation ⋮ Existence of solutions for lower semicontinuous quasi-equilibrium problems ⋮ Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions ⋮ Invex-convexlike functions and duality ⋮ Theorems of the alternative revisited and some extensions of Yuan's lemma ⋮ Errata corrige to: Stochastic differential games: Occupation measure based approach ⋮ Minimax theorems with one-sided randomization ⋮ Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings ⋮ Existence of solutions for mixed variational inequalities with perturbation in Banach spaces ⋮ General theorem on a finite support of mixed strategy in the theory of zero-sum games ⋮ Generalizations of a theorem of Arrow, Barankin, and Blackwell in topological vector spaces ⋮ Model spaces for risk measures ⋮ A probability criterion for zero-sum stochastic games ⋮ Full characterizations of minimax inequality, fixed point theorem, saddle point theorem, and KKM principle in arbitrary topological spaces ⋮ Risk minimization, regret minimization and progressive hedging algorithms ⋮ On the existence of solutions and Tikhonov regularization of hemivariational inequality problems ⋮ Generalized minimax inequalities for set-valued mappings ⋮ Coefficients of ergodicity for Markov chains with uncertain parameters ⋮ Optimal control of ellipsoidal motions ⋮ Amortized channel divergence for asymptotic quantum channel discrimination ⋮ A generalized variational principle and its application to equilibrium problems ⋮ A minimax approach for inverse variational inequalities ⋮ The existence of Nash equilibrium in \(n\)-person games with \(\mathcal C\)-concavity. ⋮ Geometry of the expected value set and the set-valued sample mean process ⋮ Existence results for strong mixed vector equilibrium problem for multivalued mappings ⋮ Efficient hedging under ambiguity in continuous time ⋮ Efficient and weak efficient points in vector optimization with generalized cone convexity ⋮ Formulae for the conjugate and the subdifferential of the supremum function ⋮ A minimax theorem for Lindelöf sets ⋮ Optimality conditions and DC-Dinkelbach-type algorithm for generalized fractional programs with ratios of difference of convex functions ⋮ Approximation of discounted minimax Markov control problems and zero-sum Markov games using Hausdorff and Wasserstein distances ⋮ Minimax theorems for extended real-valued abstract convex-concave functions ⋮ On \(\varepsilon\)-equilibrium point in a noncooperative \(n\)-person game ⋮ Minimax theorems with staircases ⋮ Weak finite intersection characterizations of existence in optimization ⋮ Modules of families of vector measures on a Riemann surface ⋮ Weighted \(L_ p\)-potential theory on homogeneous groups ⋮ Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity ⋮ Robust portfolio optimization with copulas ⋮ Generalized Knaster-Kuratowski-Mazurkiewicz theorem without convex hull ⋮ Almost monotone approximation in \(L_\infty\) ⋮ Multilayer approach to minimax theorems ⋮ A note on the Ho-problem in Hilbert space ⋮ Revisiting the Hahn-Banach theorem and nonlinear infinite programming ⋮ \(p\)-module of vector measures in domains with intrinsic metric on Carnot groups ⋮ On measurable minimax selectors ⋮ A minimax portfolio selection strategy with equilibrium ⋮ A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty ⋮ On the optimal observation problems ⋮ New generalized convexity notion for set-valued maps and application to vector optimization ⋮ Decomposition and discrete approximation methods for solving two-stage distributionally robust optimization problems ⋮ Multi-stage distributionally robust optimization with risk aversion ⋮ Dynamically consistent investment under model uncertainty: the robust forward criteria ⋮ Measures as Lagrange multipliers in multistage stochastic programming ⋮ Kolmogorov-type and general extension results for nonlinear expectations ⋮ On interval portfolio selection problem ⋮ Variational inequalities via the Hahn-Banach theorem ⋮ Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization ⋮ On classes of generalized convex functions, Gordan-Farkas type theorems, and Lagrangean duality ⋮ A symmetric minimax theorem without linear structure ⋮ Duality and regularization for inf-sup problems ⋮ Zero duality gaps in infinite-dimensional programming ⋮ Optimal estimation and control of discrete multiplicative systems with unknown second-order statistics ⋮ Minimax theorems for interval spaces ⋮ Minimax theorem and saddle point theorem without linear structure ⋮ Lagrangian multipliers for generalized affine and generalized convex vector optimization problems of set-valued maps ⋮ On an N-person noncooperative Markov game with a metric state space ⋮ New formulations of ambiguous volatility with an application to optimal dynamic contracting ⋮ Numerical solution for an inverse variational problem ⋮ The least squares estimator of random variables under convex operators on \(L_{\mathcal{F}}^\infty (\mu)\) space ⋮ On convex generalized systems ⋮ The random walk penalised by its range in dimensions \(d\geqslant 3\) ⋮ Minimax type theorems for n-valued functions ⋮ The Lagrangian, constraint qualifications and economics ⋮ Infinite zero-sum two-person games ⋮ Minimax theorems for set-valued mappings. ⋮ Doubles limites ordonnées et théorèmes de minimax ⋮ Continuity of equilibria for two-person zero-sum games with noncompact action sets and unbounded payoffs ⋮ Zero-sum semi-Markov games with state-action-dependent discount factors ⋮ Analysis of the \(N\)-card version of the game Le Her ⋮ A flexible minimax theorem ⋮ A simple proof for König's minimax theorem ⋮ A note on König's minimax theorem ⋮ Proper solutions of vector optimization problems ⋮ Convexlike and concavelike conditions in alternative, minimax, and minimization theorems ⋮ General form of the Arrow-Barabkin-Blackwell theorem in normed spaces and the \(l^ \infty\)-case ⋮ Calculus for parabolic second-order derivatives ⋮ Examples of max-flow and min-cut problems with duality gaps in continuous networks ⋮ Quantitative stability analysis for minimax distributionally robust risk optimization ⋮ A Dini-Dax theorem