## Preprint 2010-24

## Fabián Flores-Bazán, Felipe Lara:

### Inner and outer estimates for solution sets and their asymptotic cones in vector optimization

### Abstract:

We use asymptotic analysis to develop finer estimates for the efficient, weak efficient and proper efficient solution sets (and for their asymptotic cones) to a convex/quasiconvex vector optimization problems. We also provide a new representation for the efficient solution set without any convexity assumption, and the estimates involve the minima of the linear scalarization of the original vector problem. Some new necessary conditions for a point to be efficient or weak efficient solution for general convex vector optimization problems, as well as for the nonconvex quadratic multiobjective optimization, are established

This preprint gave rise to the following definitive publication(s):

**Fabián FLORES-BAZáN, Felipe LARA: ***Inner and outer estimates for solution sets and their asymptotic cones in vector optimization*. Optimization Letters, vol. 6, 7, pp. 1233-1249, (2012).