An optimality criterion for disjoint bilinear programming and its application to the problem with an acute-angled polytope for a disjoint subset

Dmitrii Lozovanu

Vladimir Andrunachievic Institute of Mathematics and Computer Science Academiei str. 5, Chişinău, MD–2028, Moldova

Abstract: We formulate and prove an optimality criterion for the disjoint bilinear programming problem and show how it can be efficiently used for solving the problem when one of the disjoint subsets has the structure of an acute-angled polytope. A class of integer and combinatorial problems that can be reduced to the disjoint bilinear programming problem with an acute-angled polytope is presented and it is shown how the considered optimality criterion can be applied.

Keywords and phrases: disjoint bilinear programming, boolean linear programming, resource allocation problem, acute angle polytope, optimality criterion.

MSC: 65K05, 68Q17, 68Q17

Received: 27.04.2024

Language: English

DOI: 10.56415/basm.y2024.i1-2.p109