On constrained optimization with nonconvex regularization

Author(s)

Birgin, E. G. ^[1] ; Martinez, J. M. ^[2] ; Ramos, A. ^[3]

Affiliation

^[1] Univ Sao Paulo, Dept Comp Sci, Inst Math & Stat, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Estadual Campinas, Dept Appl Math, Inst Math, Stat, Sci Comp, R Sergio Buarque de Holanda 651, Cidade Univ, BR-13083859 Campinas, SP - Brazil

^[3] Univ Fed Parana, Dept Math, Ctr Politecn, CP 19081, BR-81531980 Curitiba, PR - Brazil

• Document type: Journal article
• Source: NUMERICAL ALGORITHMS; v. 86, n. 3 APR 2020.
• Web of Science Citations: 0

Abstract

In many engineering applications, it is necessary to minimize smooth functions plus penalty (or regularization) terms that violate smoothness and convexity. Specific algorithms for this type of problems are available in recent literature. Here, a smooth reformulation is analyzed and equivalence with the original problem is proved both from the points of view of global and local optimization. Moreover, for the cases in which the objective function is much more expensive than the constraints, model-intensive algorithms, accompanied by their convergence and complexity theories, are introduced. Finally, numerical experiments are presented. (AU)

• FAPESP's process: 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 18/24293-0 - Computational methods in optimization
• Grantee: Sandra Augusta Santos
• Support Opportunities: Research Projects - Thematic Grants