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Risk-sensitive average optimality in Markov decision processes

Karel Sladký (2018)

Kybernetika

In this note attention is focused on finding policies optimizing risk-sensitive optimality criteria in Markov decision chains. To this end we assume that the total reward generated by the Markov process is evaluated by an exponential utility function with a given risk-sensitive coefficient. The ratio of the first two moments depends on the value of the risk-sensitive coefficient; if the risk-sensitive coefficient is equal to zero we speak on risk-neutral models. Observe that the first moment of...

Robust optimality analysis for linear programming problems with uncertain objective function coefficients: an outer approximation approach

Zhenzhong Gao, Masahiro Inuiguchi (2023)

Kybernetika

Linear programming (LP) problems with uncertain objective function coefficients (OFCs) are treated in this paper. In such problems, the decision-maker would be interested in an optimal solution that has robustness against uncertainty. A solution optimal for all conceivable OFCs can be considered a robust optimal solution. Then we investigate an efficient method for checking whether a given non-degenerate basic feasible (NBF) solution is optimal for all OFC vectors in a specified range. When the...

Robust parameter design using the weighted metric method - The case of 'the smaller the better'

Mostafa Kamali Ardakani, Rassoul Noorossana, Seyed Taghi Akhavan Niaki, Homayoun Lahijanian (2009)

International Journal of Applied Mathematics and Computer Science

In process robustness studies, it is desirable to minimize the influence of noise factors on the system and simultaneously determine the levels of controllable factors optimizing the overall response or outcome. In the cases when a random effects model is applicable and a fixed effects model is assumed instead, an increase in the variance of the coefficient vector should be expected. In this paper, the impacts of this assumption on the results of the experiment in the context of robust parameter...

Robust preconditioners for the matrix free truncated Newton method

Lukšan, Ladislav, Matonoha, Ctirad, Vlček, Jan (2010)

Programs and Algorithms of Numerical Mathematics

New positive definite preconditioners for the matrix free truncated Newton method are given. Corresponding algorithms are described in detail. Results of numerical experiments that confirm the efficiency and robustness of the preconditioned truncated Newton method are reported.

Robust real-time optimization for the linear oil blending

Stefan Janaqi, Jorge Aguilera, Meriam Chèbre (2013)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper we present a robust real-time optimization method for the online linear oil blending process. The blending process consists in determining the optimal mix of components so that the final product satisfies a set of specifications. We examine different sources of uncertainty inherent to the blending process and show how to address this uncertainty applying the Robust Optimization techniques. The polytopal structure of our problem permits a simplified robust approach. Our method is intended...

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