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Stability and Sensitivity of Uncertain Linear Programs
The present paper deals with uncertain linear optimization problems where the objective function coefficient vector belongs to a compact convex...
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Artificial neural networks with uniform norm-based loss functions
We explore the potential for using a nonsmooth loss function based on the max-norm in the training of an artificial neural network without hidden...
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An Algorithm for Best Generalised Rational Approximation of Continuous Functions
In this paper we introduce an algorithm for solving variational inequality problems when the operator is pseudomonotone and point-to-set (therefore...
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Approximations of Quasi-Equilibria and Nash Quasi-Equilibria in Terms of Variational Convergence
Various types of variational convergence of functions and bifunctions are applied to study global approximations of a quasi-equilibrium problem and a...
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Conservative Parametric Optimality and the Ridge Method for Tame Min-Max Problems
We study the ridge method for min-max problems, and investigate its convergence without any convexity, differentiability or qualification assumption....
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Some minimax problems in lexicographic order
In this paper, minimax theorems and saddle points for a class of vector-valued map**s f ( x , y ) = u ( x )+ β ( x ) v ( y ) are first investigated in the sense...
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The Penalty Functions Method and Multiplier Rules Based on the Mordukhovich Subdifferential
We show that the finite-dimensional Fritz John multiplier rule, which is based on the limiting/Mordukhovich subdifferential, can be proved by using...
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Evolution of the 1984 KKM theorem of Ky Fan
Recently we established the Knaster, Kuratowski, and Mazurkiewicz (KKM) theory on abstract convex spaces. In our research, we noticed that there are...
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Ky Fan minimax inequalities for set-valued map**s
In this article, by virtue of the Kakutani-Fan-Glicksberg fixed point theorem, two types of Ky Fan minimax inequalities for set-valued map**s are...
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Minimax theorems for scalar set-valued map**s with nonconvex domains and applications
In this paper, by virtue of the separation theorem of convex sets, we prove a minimax theorem, a cone saddle point theorem and a Ky Fan minimax...
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A strict minimax inequality criterion and some of its consequences
In this paper, we point out a very flexible scheme within which a strict minimax inequality occurs. We then show the fruitfulness of this approach...
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A classical decision theoretic perspective on worst-case analysis
We examine worst-case analysis from the standpoint of classical Decision Theory. We elucidate how this analysis is expressed in the framework...
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Randomized first order algorithms with applications to ℓ 1-minimization
In this paper we propose randomized first-order algorithms for solving bilinear saddle points problems. Our developments are motivated by the need...
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On Diagonal Subdifferential Operators in Nonreflexive Banach Spaces
Consider a real-valued bifunction f defined on C × C , where C is a closed and convex subset of a Banach space X , which is concave in its first...
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Minimax inequalities for set-valued map**s
In this paper, by using the finite intersection property, we first obtain two types of minimax inequalities for set-valued map**s, which improve...
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Packing directed circuits exactly
We give an “excluded minor” and a “structural” characterization of digraphs D that have the property that for every subdigraph H of D , the maximum...
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Minimax strategies and duality with applications in financial mathematics
Many topics in Actuarial and Financial Mathematics lead to Minimax or Maximin problems (risk measures optimization, ambiguous setting, robust...
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Semi-Markov Control Models with Partially Known Holding Times Distribution: Discounted and Average Criteria
The paper deals with a class of semi-Markov control models with Borel state and control spaces and possibly unbounded costs, where the holding times...