Global Optimization for Generalized Linear Multiplicative Programming Using Convex Relaxation

Global optimization of a generalized linear multiplicative program

In this paper a solution algorithm for a class of generalized linear multiplicative programs having a polyhedral feasible region is proposed. The algorithm is based on the so called optimal level solutions method. Some optimality conditions are used to improve the performance of the proposed algorithm. Results of a computational test are provided.

Generalized Convex Disjunctive Programming: Nonlinear Convex Hull Relaxation

Convex Programming Methods for Global Optimization

We investigate some approaches to solving nonconvex global optimization problems by convex nonlinear programming methods. We assume that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We provide a survey of disjunctive programming with convex relaxations, logic-based outer approximation, and logi...

Global optimization of generalized linear fractional programming with nonlinear constraints

This paper presents a branch-and-bound algorithm for globally solving a wide class of generalized linear fractional programming problems (GLFP). This class includes such problems as: minimizing a sum, or error for product of a finite number of ratios of linear functions, linear multiplicative programming, polynomial programming, etc. – over nonconvex feasible region. First a problem (Q) is deri...

A Global Algorithm for Quadratic Programming with One Negative Eigenvalue Based on Successive Linear Conic Optimization and Convex Relaxation

We consider quadratic programs with a single negative eigenvalue (QP1NE) subject to linear and conic constraints. The QP1NE model covers the classical clique problem that is known to be NP-hard [26]. In this paper, by combining successive linear conic optimization (SLCO), convex relaxation and line search technique, we present a global algorithm for QP1NE which can locate a global optimal solut...