Generalized problem of linear copositive programming
https://doi.org/10.29235/1561-2430-2019-55-3-299-308
Abstract
We consider a special class of optimization problems where the objective function is linear w.r.t. decision variable х and the constraints are linear w.r.t. х and quadratic w.r.t. index t defined in a given cone. The problems of this class can be considered as a generalization of semi-definite and copositive programming problems. For these problems, we formulate an equivalent semi-infinite problem and define a set of immobile indices that is either empty or a union of a finite number of convex bounded polyhedra. We have studied properties of the feasible sets of the problems under consideration and use them to obtain new efficient optimality conditions for generalized copositive problems. These conditions are CQ-free and have the form of criteria.
Supporting agencies: This work was partially supported by the state research program “Convergence” (Republic Belarus), Task 1.3.01 and by Portuguese funds through CIDMA – Center for Research and Development in Mathematics and Applications, and FCT – Portuguese Foundation for Science and Technology, within the project UID/MAT/04106/2019.
About the Authors
O. I. Kostyukova
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Olga I. Kostyukova – Dr. Sc. (Physics and Mathematics), Full Professor, Principal Research Fellow
11, Surganov Str., 220072, Minsk, Republic of Belarus
T. V. Tchemisova
University of Aveiro
Portugal
Portugal
Tchemisova Tatiana Vladimirovna – Ph. D. (Physics and Mathematics), Assistant Professor of the Department of Mathematics
Campus Universitário Santiago, 3800-192, Aveiro, Portugal
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