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57. Multi-Objective Nonlinear Conjugate Gradient Schemes with Guaranteed Descent
Invited abstract in session TB-37: Advances in Continuous Multiobjective Optimization, stream Multiobjective Optimization.
Tuesday, 10:30-12:00Room: 33 (building: 306)
Authors (first author is the speaker)
| 1. | Manuel Berkemeier
|
| Computer Science, TU Dortmund University | |
| 2. | Sebastian Peitz
|
| Department of Computer Science, University of Paderborn |
Abstract
Various nonlinear Conjugate Gradient (CG) schemes have been observed to improve convergence rates in single-objective optimization compared to steepest descent, without requiring second-order derivatives. Pérez and Prudente translated many of the most popular CG directions to the multi-objective case. However, in order to prove convergence, the classical CG schemes require us to assume Wolfe conditions on the step-size. In some settings, fulfilling Wolfe conditions might not be possible. Thus, we present several example directions that provide guaranteed descent in all objective functions, independent of the step-size. This enables us to prove convergence to Pareto-critical points for a simple inexact line-search algorithm with backtracking to satisfy some modified Armijo-rule.
Our special CG directions are designed to be implementable without too much computational cost, and numerical experiments show the efficacy of the algorithm.
Keywords
- Programming, Multi-Objective
- Continuous Optimization
- Programming, Linear
Status: accepted
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