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In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of -transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type of -transformations....
In this paper, the robust counterpart of the linear fractional programming problem under linear inequality constraints with the interval and ellipsoidal uncertainty sets is studied. It is shown that the robust counterpart under interval uncertainty is equivalent to a larger linear fractional program, however under ellipsoidal uncertainty it is equivalent to a linear fractional program with both linear and second order cone constraints. In addition, for each case we have studied the dual problems...
In this paper, the linear programming problem subject to the Bipolar Fuzzy Relation Equation (BFRE) constraints with the max-parametric hamacher composition operators is studied. The structure of its feasible domain is investigated and its feasible solution set determined. Some necessary and sufficient conditions are presented for its solution existence. Then the problem is converted to an equivalent programming problem. Some rules are proposed to reduce the dimensions of problem. Under these rules,...
The standard multiple criteria optimization starts with an
assumption that the criteria are incomparable. However, there are many
applications in which the criteria express ideas of allocation of
resources meant to achieve some equitable distribution. This paper
focuses on solving linear multiple criteria optimization problems with
uniform criteria treated in an equitable way. An axiomatic definition of
equitable efficiency is introduced as an refinement of
Pareto-optimality. Various generation...
In this paper we investigate a class of problems permitting a good characterisation from the point of view of morphisms of oriented matroids. We prove several morphism-duality theorems for oriented matroids. These generalize LP-duality (in form of Farkas' Lemma) and Minty's Painting Lemma. Moreover, we characterize all morphism duality theorems, thus proving the essential unicity of Farkas' Lemma. This research helped to isolate perhaps the most natural definition of strong maps for oriented matroids....
We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].
We discuss some implications of linear programming for Mather theory
[13-15] and its
finite dimensional approximations. We find that the complementary
slackness condition of duality theory formally implies that the Mather set lies in an
n-dimensional graph and as well predicts the relevant nonlinear PDE for the “weak
KAM” theory of Fathi [5-8].
We are concerned with the Lipschitz modulus of the optimal set mapping associated with canonically perturbed convex semi-infinite optimization problems. Specifically, the paper provides a lower and an upper bound for this modulus, both of them given exclusively in terms of the problem’s data. Moreover, the upper bound is shown to be the exact modulus when the number of constraints is finite. In the particular case of linear problems the upper bound (or exact modulus) adopts a notably simplified...
We are concerned with the Lipschitz modulus of the optimal set mapping
associated with canonically perturbed convex semi-infinite optimization
problems. Specifically, the paper provides a lower and an upper bound for
this modulus, both of them given exclusively in terms of the problem's data.
Moreover, the upper bound is shown to be the exact modulus when the number
of constraints is finite. In the particular case of linear problems the
upper bound (or exact modulus) adopts a notably simplified...
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