2022/07/25 by Rosa Donat, Donat, Rosa, Sergio López Ureña +1
Computer Science · Decision Sciences · Mathematics · #65D05 #65K10 #90C26 #90C56 #Advanced Multi-Objective Optimization Algorithms #Advanced Optimization Algorithms Research #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2207.12136
openalex publication_date 2022/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
General purpose optimization techniques can be used to solve many problems in engineering computations, although their cost is often prohibitive when the number of degrees of freedom is very large. We describe a multilevel approach to speed up the computation of the solution of a large-scale optimization problem by a given optimization technique. By embedding the problem within Harten's Multiresolution Framework (MRF), we set up a procedure that leads to the desired solution, after the computation of a finite sequence of sub-optimal solutions, which solve auxiliary optimization problems involving a smaller number of variables. For convex optimization problems having smooth solutions, we prove that the distance between the optimal solution and each sub-optimal approximation is related to the accuracy of the interpolation technique used within the MRF and analyze its relation with the performance of the proposed algorithm. Several numerical experiments confirm that our technique provides a computationally efficient strategy that allows the end user to treat both the optimizer and the objective function as black boxes throughout the optimization process.