Open AccessGeneralized problem of linear copositive programming
Author(s) -
О. И. Костюкова,
Т. В. Чемисова
Publication year - 2019
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2019-55-3-299-308
Subject(s) - mathematics , generalization , class (philosophy) , bounded function , polyhedron , linear programming , combinatorics , regular polygon , mathematical optimization , function (biology) , optimization problem , discrete mathematics , mathematical analysis , computer science , geometry , artificial intelligence , evolutionary biology , biology
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.