Discounted dynamic programming on Euclidean spaces
A. Nowak (1979)
Applicationes Mathematicae
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A. Nowak (1979)
Applicationes Mathematicae
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Rolando Cavazos-Cadena, Raul Montes-de-Oca (2001)
Applicationes Mathematicae
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This work concerns Markov decision processes with finite state space and compact action sets. The decision maker is supposed to have a constant-risk sensitivity coefficient, and a control policy is graded via the risk-sensitive expected total-reward criterion associated with nonnegative one-step rewards. Assuming that the optimal value function is finite, under mild continuity and compactness restrictions the following result is established: If the number of ergodic classes when a stationary...
Zhu, Quanxin, Guo, Xianping (2006)
Journal of Applied Mathematics and Stochastic Analysis
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R. Israel Ortega-Gutiérrez, Raúl Montes-de-Oca, Enrique Lemus-Rodríguez (2016)
Kybernetika
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Many examples in optimization, ranging from Linear Programming to Markov Decision Processes (MDPs), present more than one optimal solution. The study of this non-uniqueness is of great mathematical interest. In this paper the authors show that in a specific family of discounted MDPs, non-uniqueness is a “fragile” property through Ekeland's Principle for each problem with at least two optimal policies; a perturbed model is produced with a unique optimal policy. This result not only supersedes...
Petr Fiala (2011)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Mathematical programming under multiple objectives has emerged as a powerful tool to assist in the process of searching for decisions which best satisfy a multitude of conflicting objectives. In multiobjective linear programming problems it is usually impossible to optimize all objectives in a given system. Trade-offs are properties of inadequately designed system a thus can be eliminated through designing better one. Multiobjective De Novo linear programming is problem for designing...
Jussi Hakanen, Yoshiaki Kawajiri, Kaisa Miettinen, Lorenz Biegler (2007)
Control and Cybernetics
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H. Girlich (1980)
Banach Center Publications
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Tadeusz Antczak (2009)
Applications of Mathematics
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A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between...
Ilija Nikolić (2007)
The Yugoslav Journal of Operations Research
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Krzysztof Szajowski (2010)
Banach Center Publications
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The following problem in risk theory is considered. An insurance company, endowed with an initial capital a > 0, receives insurance premiums and pays out successive claims from two kind of risks. The losses occur according to a marked point process. At any time the company may broaden or narrow down the offer, which entails the change of the parameters of the underlying risk process. These changes concern the rate of income, the intensity of the renewal process and the distribution...