Optimizing the sum of linear fractional functions
Recent advances in global optimization
Minimizing and maximizing the product of linear fractional functions
Recent advances in global optimization
Linear multiplicative programming
Mathematical Programming: Series A and B
Minimization of the sum of three linear fractional functions
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its 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
Optimization of Polynomial Fractional Functions
Journal of Global Optimization
Global optimization for sum of generalized fractional functions
Journal of Computational and Applied Mathematics
Solving the sum-of-ratios problem by a stochastic search algorithm
Journal of Global Optimization
A nonisolated optimal solution of general linear multiplicative programming problems
Computers and Operations Research
Global optimization for a class of fractional programming problems
Journal of Global Optimization
A FPTAS for a class of linear multiplicative problems
Computational Optimization and Applications
A numerical study on B&B algorithms for solving sum-of-ratios problem
AST/UCMA/ISA/ACN'10 Proceedings of the 2010 international conference on Advances in computer science and information technology
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This paper is concerned with a practical algorithm for solving low rank linear multiplicative programming problems and low rank linear fractional programming problems. The former is the minimization of the sum of the product of two linear functions while the latter is the minimization of the sum of linear fractional functions over a polytope. Both of these problems are nonconvex minimization problems with a lot of practical applications. We will show that these problems can be solved in an efficient manner by adapting a branch and bound algorithm proposed by Androulakis–Maranas–Floudas for nonconvex problems containing products of two variables. Computational experiments show that this algorithm performs much better than other reported algorithms for these class of problems.