5. Effective Front-Descent Algorithms with Convergence Guarantees
Invited abstract in session TC-10: Continuous Multi-Objective Optimization: Algorithms and Complexity Analyses, stream Multiobjective and Vector Optimization.
Tuesday, 14:00-16:00Room: B100/8011
Authors (first author is the speaker)
| 1. | Matteo Lapucci
|
| Department of Information Engineering, University of Florence | |
| 2. | Pierluigi Mansueto
|
| Department of Information Engineering, University of Florence | |
| 3. | Davide Pucci
|
| Department of Information Engineering, University of Florence |
Abstract
We address continuous unconstrained multi-objective optimization problems and we discuss descent type methods for the reconstruction of the Pareto set. Specifically, we describe the class of Front Descent methods, which generalizes the Front Steepest Descent algorithm allowing the employment of suitable, effective search directions (e.g., Newton, Quasi-Newton, Barzilai-Borwein). We give a deep characterization of the behavior and the mechanisms of the algorithmic framework, and we underline how, under reasonable assumptions, standard convergence results and some complexity bounds hold for the generalized approach. Moreover, we remark that popular search directions can indeed be soundly used within the framework. We furthermore present a completely novel type of convergence results, concerning the sequence of sets produced by the procedure. These results concern convergence to stationarity for any sequence of induvidual points in these sets; additionally, some interesting properties are discovered that are useful in finite precision settings. Finally, the results from a large experimental benchmark are shown.
Keywords
- Multi-objective optimization
Status: accepted
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