Institute of Information Theory and Automation

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Publication details

A remark on multiobjective stochastic optimization via strongly convex functions

Journal Article

Kaňková Vlasta

serial: Central European Journal of Operations Research vol.24, 2 (2016), p. 309-333

project(s): GA13-14445S, GA ČR

keywords: Stochasticmultiobjective optimization problem, Efficient solution, Wasserstein metric and L_1 norm, Stability and empirical estimates

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abstract (eng):

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.


bocek: 2012-12-21 16:10