Global minimization of large-scale constrained concave quadratic problems by separable programming
Mathematical Programming: Series A and B
An algorithm for global minimization of linearly constrained concave quadratic functions
Mathematics of Operations Research
Journal of Global Optimization
Minimization of the sum of three linear fractional functions
Journal of Global Optimization
Journal of Global Optimization
Solving the Sum-of-Ratios Problem by an Interior-Point Method
Journal of Global Optimization
Conical Partition Algorithm for Maximizing the Sum of dc Ratios
Journal of Global Optimization
A Revision of the Trapezoidal Branch-and-Bound Algorithm for Linear Sum-of-Ratios Problems
Journal of Global Optimization
Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
Solving the sum-of-ratios problem by a stochastic search algorithm
Journal of Global Optimization
Triangulation of Points, Lines and Conics
Journal of Mathematical Imaging and Vision
A simplicial branch and duality bound algorithm for the sum of convex-convex ratios problem
Journal of Computational and Applied Mathematics
Global optimization for a class of fractional programming problems
Journal of Global Optimization
Solving the sum-of-ratios problems by a harmony search algorithm
Journal of Computational and Applied Mathematics
Triangulation of points, lines and conics
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
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
Global optimization for the generalized polynomial sum of ratios problem
Journal of Global Optimization
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
A practical but rigorous approach to sum-of-ratios optimization in geometric applications
Computational Optimization and Applications
Hi-index | 0.03 |
This article presents a branch and bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm works by globally solving a sum of ratios problem that is equivalent to problem (P). In the algorithm, upper bounds are computed by maximizing concave envelopes of a sum of ratios function over intersections of the feasible region of the equivalent problem with rectangular sets. The rectangular sets are systematically subdivided as the branch and bound search proceeds. Two versions of the algorithm, with convergence results, are presented. Computational advantages of these algorithms are indicated, and some computational results are given that were obtained by globally solving some sample problems with one of these algorithms.