A remark on multiobjective stochastic optimization via strongly convex functions

0450553 - ÚTIA 2017 RIV DE eng J - Journal Article
Kaňková, Vlasta
A remark on multiobjective stochastic optimization via strongly convex functions.
Central European Journal of Operations Research. Roč. 24, č. 2 (2016), s. 309-333. ISSN 1435-246X. E-ISSN 1613-9178
R&D Projects: GA ČR GA13-14445S
Institutional support: RVO:67985556
Keywords : Stochasticmultiobjective optimization problem * Efficient solution * Wasserstein metric and L_1 norm * Stability and empirical estimates
Subject RIV: BB - Applied Statistics, Operational Research
Impact factor: 0.659, year: 2016
http://library.utia.cas.cz/separaty/2015/E/kankova-0450553.pdf

Many economic and financial applications lead (from the mathematical point of view) to deterministic optimization problems depending on a probability measure. These problems can be static (one stage), dynamic with finite (multistage) or infinite horizon, single objective or multiobjective. We focus on one-stage case in multiobjective setting. Evidently, well known results from the deterministic optimization theory can be employed in the case when the "underlying" probability measure is completely known. The assumption of a complete knowledge of the probability measure is fulfilled very seldom. Consequently, we have mostly to analyze the mathematical models on the data base to obtain a stochastic estimate of the corresponding "theoretical" characteristics. However, the investigation of these estimates has been done mostly in one-objective case. In this paper we focus on the investigation of the relationship between "characteristics" obtained on the base of complete knowledge of the probability measure and estimates obtained on the (above mentioned) data base, mostly in the multiobjective case.
Permanent Link: http://hdl.handle.net/11104/0252048