2011/02/24 by Florian Bugarin, Didier Henrion, Bugarin, Florian +3 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Numerical Methods and Algorithms #Optimization and Control (math.OC) #Polynomial and algebraic computation #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1102.4954
openalex publication_date 2011/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of variables can be large (10 to 100) provided some kind of sparsity is present. We describe a formulation of the rational optimization problem as a generalized moment problem and its hierarchy of convex semidefinite relaxations. Under some conditions we prove that the sequence of optimal values converges to the globally optimal value. We show how public-domain software can be used to model and solve such problems.