Generalized linear multiplicative and fractional programming
Annals of Operations Research
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Optimizing the sum of linear fractional functions
Recent advances in global optimization
An interior point method for multifractional programs with convex constraints
Journal of Optimization Theory and Applications
An interior-point method for fractional programs with convex constraints
Mathematical Programming: Series A and B
On polynomiality of the method of analytic centers for fractional problems
Mathematical Programming: Series A and B
On self-concordant barrier functions for conic hulls and fractional programming
Mathematical Programming: Series A and B
Voronoi diagrams and Delaunay triangulations
Handbook of discrete and computational geometry
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
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
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
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 QCQP approach to triangulation
ECCV'12 Proceedings of the 12th 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 | 0.00 |
We consider the problem of minimizing the sum of a convex function and of p≥1 fractions subject to convex constraints. The numerators of the fractions are positive convex functions, and the denominators are positive concave functions. Thus, each fraction is quasi-convex. We give a brief discussion of the problem and prove that in spite of its special structure, the problem is \cN\cP-complete even when only p=1 fraction is involved. We then show how the problem can be reduced to the minimization of a function of p variables where the function values are given by the solution of certain convex subproblems. Based on this reduction, we propose an algorithm for computing the global minimum of the problem by means of an interior-point method for convex programs.