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Problém dvou manažérů a problematika úloh stochastického programování s lineární kompenzací
Kaňková, Vlasta
Stochastic programming problems with linear recourse correspond to many economic problems. It is generally known that these problems are a composition of two (outer and inner) optimization problems. A solution of the outer problem depends on an ``underlying" probability measure while a solution of the inner problem depends on the solution of the outer problem and on the random element realization. Evidently, a position and optimal behaviour of two managers can be (in many cases) described by this type of the model in which the optimal behaviour of the main manager is determined by the outer problem while the optimal behaviour of the second manager is described by the inner problem. We focus on an investigation of properties of the inner problem.
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Ramseův růstový model: zobecnění a algoritmická řešení
Sladký, Karel
We consider in discrete-time finite state approximations of an extended Ramsey type model under stochastic uncertainty. Recalling standard procedure of stochastic dynamic programming we present explicit formulas for finding maximum global utility of the consumers (i.e. sum of total discounted instantaneous utilities) in the approximated model along with error bounds of the approximations.
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Empirické odhady a stabilita ve stochastickém programování
Kaňková, Vlasta
It is known that optimization problems depending on a probability measure correspond to many applications. It is also known that these problems belong mostly to a class of nonlinear optimization problems and, moreover, that very often an ``underlying" probability measure is not completely known. The aim of the research report is to deal with the case when an empirical measure substitutes the theoretical one. In particular, the aim is to generalize reults dealing with convergence rate in the case of empirical esrimates. The introduced results are based on the stability results corresponding to the Wasserstein metric. A relationship berween tails of one-dimensional marginal distribution functions and exponentional rate of convergence are introduced. The corresponding results are focus mainly on ``classical" type of problems corresponding to the cases with penalty and recourse. However, an integer simple recourse case and some special risk funkcionals are discussed also.
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Porovnání aproximací v úlohách stochastické a robustní optimalizace
Houda, Michal
The paper deals with two wide areas of optimization theory: stochastic and robust programming. We specialize to different approaches when solving an optimization problem where some uncertainties in constraints occur. To overcome uncertainty, we can request the solution to be feasible to all but a small part of constraints. Both approaches gives us different methods to deal with this requirement. We try to find fundamental differencies between them and illustrate the differencies on a simple numerical example.
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Úlohy stochastického programování s lineární kompensací: Aplikace na problematiku dvou manažérů
Kaňková, Vlasta
Stochastic programming problems with recourse are a composition of two (outer and inner) optimization problems. A solution of the outer problem depends on the "underlying" probability measure while a solution of the inner problem depends on the solution of the outer problem and on the random element realization. Evidently, a position and optimal behaviour of two managers can (in many cases) be described by this type of the model in which an optimal behaviour of the main manager is determined by the outer problem while the optimal behaviour of the second manager is described by the inner problem. We focus on an investigation of the inner problem.
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Aproximace ve stochastických růstových modelech
Sladký, Karel
In this note, we consider finite state approximations of the stochastic Ramsey type model in discrete-time version. Recalling standard procedures of stochastic dynamic programming we present explicit formulas for finding maximum global utility of the consumers (i.e. sum of total discounted instantaneous utilies) in the approximated model.
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Aproximace stochastických a robustních optimalizačních úloh
Houda, Michal
The paper deals with two wide areas of optimization theory: stochastic and robust programming. We specialize to different approaches when solving an optimization problem where some uncertainties in constraints occur. To overcome uncertainty, we can request the solution to be feasible to all but a small part of constraints. Both approaches gives us different methods to deal with this requirement. We try to find fundamental differencies between them and illustrate the differencies on a simple numerical example.
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Empirické procesy ve stochastickém programování
Kaňková, Vlasta ; Houda, Michal
Usually, it is very complicated to investigate and to solve optimization problems depending on a probability measure. To this end a stability of them, considers with respect to a prabability measure space, has been discused in the stochastic programming literature many times. The paper is focus on the investigation of the stability with respect to the Wasserstein and to the Komolgorov metrics with "underlying" L_1 space. Moreover, we applay achieved stability results to empirical estimates.
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