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3297. Combining interior and exterior penalty for nonlinear costrained black-box optimization problems
Invited abstract in session MA-32: Large Scale Constrained Optimization: Algorithms and Applications, stream Advances in large scale nonlinear optimization.
Monday, 8:30-10:00Room: 41 (building: 303A)
Authors (first author is the speaker)
| 1. | Andrea Brilli
|
| Department of Computer Control and Management Engineering “A. Ruberti”, Sapienza University of Rome | |
| 2. | Everton Silva
|
| Mathematics, NOVA School of Science and Technology | |
| 3. | Ana Luisa Custodio
|
| Dept. Mathematics, Universidade Nova de Lisboa | |
| 4. | Giampaolo Liuzzi
|
| DIAG - Sapienza University of Rome |
Abstract
This research explores an approach to addressing mathematical optimization problems characterized by nonlinear objective functions and constraints, particularly in situations where derivatives are unavailable. A Sequential Penalty Approach is introduced, incorporating a Logarithmic Barrier for managing inequality constraints and an Exterior Penalty for equality constraints. Our proposed method aims to providing a comprehensive solution for a wide range of nonlinear optimization challenges.
This strategy, proposed for the first time in a derivative-free setting in the framework of linesearch methods, is adapted and incorporated into SID-PSM algorithm, a generalized pattern search method, allowing to effectively handle general nonlinear constraints. Under reasonable assumptions regarding the smoothness of the functions, convergence is established, without any convexity assumption.
Empirical validation is conducted through experimentation on a diverse set of optimization problems. The results corroborate not only the efficacy of the proposed approach but also its practical utility. The direct search algorithm, when complemented by the Logarithmic Barrier and Exterior Penalty, consistently exhibits promising numerical results, demonstrating the potential of the techinque.
Keywords
- Continuous Optimization
- Interior Point Methods
- Programming, Nonlinear
Status: accepted
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