Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis

Details Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis

2010-01-30

arxiv.org/abs/1002.0093v2

SIAM J. Optim. 21, pp. 463-490 2011

Mathematics

Optimization and Control

29 pages, 12 figures

Scientific paper

10.1137/100784746

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hierarchy between singular set, Pareto critical set and stable Pareto critical set, and can handle the problem of superposition of local Pareto fronts, occurring in the general nonconvex case. Furthermore, a quadratic convergence result in a suitable set-wise sense is proven and tested in a number of numerical examples.

Affiliated with

Also associated with

No associations

Rating

Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-346885