2022/11/28 by Renan Spencer Trindade, Claudia D’Ambrosio, Trindade, Renan Spencer +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Multi-Criteria Decision Making #Optimization and Control (math.OC) #Peroxisome Proliferator-Activated Receptors
paper · doi:10.48550/arxiv.2211.15450
openalex publication_date 2022/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our study is motivated by the solution of Mixed-Integer Non-Linear Programming (MINLP) problems with separable non-convex functions via the Sequential Convex MINLP technique, an iterative method whose main characteristic is that of solving, for bounding purposes, piecewise-convex MINLP relaxations obtained by identifying the intervals in which each univariate function is convex or concave and then relaxing the concave parts with piecewise-linear relaxations of increasing precision. This process requires the introduction of new binary variables for the activation of the intervals where the functions are defined. In this paper we compare the three different standard formulations for the lower bounding subproblems and we show, both theoretically and computationally, that -- unlike in the piecewise-linear case -- they are not equivalent when the perspective reformulation is applied to reinforce the formulation in the segments where the original functions are convex.