Polynomial algorithm for the disjoint bilinear programming problem with an acute-angled polytope for a disjoint subset

TL;DR

This paper introduces a polynomial algorithm for solving a specific class of disjoint bilinear programming problems where one subset forms an acute-angled polytope, with applications to boolean and piecewise linear concave programming.

Contribution

The paper formulates an optimality criterion and develops a polynomial algorithm tailored for disjoint bilinear programming problems with an acute-angled polytope structure.

Findings

The algorithm is proven to be polynomial in complexity.

It can be effectively applied to boolean linear programming.

It extends to piecewise linear concave programming.

Abstract

We consider the disjoint bilinear programming problem in which one of the disjoint subsets has the structure of an acute-angled polytope. An optimality criterion for such a problem is formulated and proved, and based on this, a polynomial algorithm for its solving is proposed and grounded. We show that the proposed algorithm can be efficiently used for studying and solving the boolean linear programming problem and the piecewise linear concave programming problem.