Generalized linear multiplicative and fractional programming
Annals of Operations Research
Linear multiplicative programming
Mathematical Programming: Series A and B
Finite algorithm for generalized linear multiplicative programming
Journal of Optimization Theory and Applications
Multiplicative programming problems: analysis and efficient point search heuristic
Journal of Optimization Theory and Applications
Generalized Convex Multiplicative Programming via QuasiconcaveMinimization
Journal of Global Optimization
On finding most optimal rectangular package plans
DAC '82 Proceedings of the 19th Design Automation Conference
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
A Finite Branch-and-Bound Algorithm for Linear Multiplicative Programming
Computational Optimization and Applications
Using concave envelopes to globally solve the nonlinear sum of ratios problem
Journal of Global Optimization
Global optimization algorithm for the nonlinearsum of ratios problem
Journal of Optimization Theory and Applications
A convex analysis approach for convex multiplicative programming
Journal of Global Optimization
A nonisolated optimal solution of general linear multiplicative programming problems
Computers and Operations Research
A FPTAS for a class of linear multiplicative problems
Computational Optimization and Applications
An outcome space approach for generalized convex multiplicative programs
Journal of Global Optimization
Global optimization of convex multiplicative programs by duality theory
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
An objective space cut and bound algorithm for convex multiplicative programmes
Journal of Global Optimization
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This article presents a new global solution algorithm for Convex Multiplicative Programming called the Outcome Space Algorithm. To solve a given convex multiplicative program (PD), the algorithm solves instead an equivalent quasiconcave minimization problem in the outcome space of the original problem. To help accomplish this, the algorithm uses branching, bounding and outer approximation by polytopes, all in the outcome space of problem (PD). The algorithm economizes the computations that it requires by working in the outcome space, by avoiding the need to compute new vertices in the outer approximation process, and, except for one convex program per iteration, by requiring for its execution only linear programming techniques and simple algebra.