### Tibor Illés (Eötvös Loránd University, Budapest)

#### Approximation of the whole Pareto-optimal solution set for vector optimization problems

*Joint work with Gábor Lovics.*

*Thursday 7 March 2013 at 13.00, TBA*

##### Abstract

In economic and engineering application of mathematics sometimes we need to
optimize more than one objective function at the same time. In this type of
problems we need to find solutions, where one of the objectives can not be
improved without worsen the other. These solutions are called Pareto-optimal
solutions, and since 1950's such methods are known to compute one of the
Pareto-optimal solutions.

Recently, for unconstrained multi objective optimization problems such
algorithm has been developed by Oliver Schütze at al. (2003) that try to
approximate the whole set of the Pareto-optimal solutions. In this talk we
generalize the subdivision algorithm of Schütze and others for linearly
constrained multi objective optimization problem. The objective functions in
our case need to be differentiable convex functions. The main idea of the
method to find feasible joint decreasing direction, for the objective
functions. Further generalization of the more general class of problems
(convex constrained and convex objective function for mineralization problem)
seems to be possible. Practical applicability of the new algorithm has tested
on the Markowitz portfolio optimization problem.

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