1569. A Newton-type method for non-smooth vector optimization
Invited abstract in session TD-51: Advances in nonlinear multiobjective optimization, stream Multiobjective and vector optimization.
Tuesday, 14:30-16:00Room: Parkinson B22
Authors (first author is the speaker)
| 1. | Titus Pinta
|
| Mathematics, ENSTA |
Abstract
We propose a new algorithm for determining efficient solutions to non-smooth multiobjective optimization problems based on Newton's method. The key insight comes from the fact that the search for such points can be recast into a problem of finding the roots of an underdetermined system of equations, with half of the variables lying in the standard simplex. Then, the classic Newton algorithm can be easily generalized to the underdetermined framework by employing pseudo-inverses, while the constraints can be handled by simple projections. This algorithm is then extended to work with arbitrary partial orderings induced by convex cones by replacing the simplex constraints with more general ones. In order to handle non-smooth problems, the notion of Newton differentiability suffices for the analysis of the algorithm, which achieves super-linear convergence. To showcase the algorithm, numerical tests are provided, illustrating the fact that the proposed method, while resembling a scalarization technique, does not fail in the well-known pathological counter-examples to such techniques.
Keywords
- Programming, Multi-Objective
- Non-smooth Optimization
Status: accepted
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