342. Stochastic approximation in convex multiobjective optimization
Invited abstract in session WC-10: Computational Aspects in Multiobjective Optimization, stream Multiobjective and Vector Optimization.
Wednesday, 14:00-16:00Room: B100/8011
Authors (first author is the speaker)
| 1. | Elena Molho
|
| Dipartimento di Scienze Economiche e Aziendali, Università di Pavia | |
| 2. | Carlo Alberto De Bernardi
|
| Department of Mathematical Sciences, Mathematical Finance and Econometrics, Università Cattolica del Sacro Cuore | |
| 3. | Enrico Miglierina
|
| Dipartimento di Dipartimento di Matematica per le scienze economiche, finanziarie ed attuariali, Universita Cattolica del Sacro Cuore | |
| 4. | Jacopo Somaglia
|
| Dipartimento di Matematica, Politecnico di Milano |
Abstract
Given a multiobjective optimization problem with N strictly convex objective functions, we focus on a minimizer obtained by a linear scalarization technique with a specific choice of the coefficients in the simplex. Our main result is to find an estimation of the averaged error that we make if we approximate that minimizer with the minimizers of the convex combinations of n functions randomly chosen among the original N objective functions with probabilities that coincide with the original scalarization coefficients and uniformly weighted by the reciprocal of n. We prove that the averaged error considered above converges to 0 uniformly with respect to the coefficients.
The key tool in the proof of our stochastic approximation theorem is a geometrical property, called small diameter property, ensuring that the minimizer of a convex combination of the objective functions continuously depends on the coefficients of the convex combination.
Keywords
- Multi-objective optimization
Status: accepted
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