On the convergence rate of empirical estimates in chance constrained stochastic programming
Stability in stochastic programming -- The case of unknown location parameter
Stability in the stochastic programming
Necessary and sufficient optimality conditions for two-stage stochastic programming problems
Optimization problem with parameter and its application to the problems of two-stage stochastic nonlinear programming
On the stability in stochastic programming: the case of individual probability constraints
A note on the differentiability in two-stage stochastic nonlinear programming problems
Multistage stochastic programs via autoregressive sequences and individual probability constraints
The paper deals with a special case of multistage stochastic programming problems. In particular, the paper deals with multistage stochastic programs in which a random element follows an autoregressive sequence and constraint sets correspond to the individual probability constraints. The aim is to investigate a stability (considered with respect to a probability measures space) and empirical estimates. To achieve new results the Wasserstein metric determined by norm and results of multiobjective...
Empirical estimates in stochastic optimization via distribution tails
“Classical” optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are, from the numerical point of view, relatively complicated. On the other hand, these problems fulfil very often assumptions giving a possibility to replace the “underlying” probability measure by an empirical one to obtain “good” empirical estimates of the optimal value and the optimal solution. Convergence rate of these estimates have been studied mostly for...
Stability, empirical estimates and scenario generation in stochastic optimization - applications in finance
Economic and financial processes are mostly simultaneously influenced by a random factor and a decision parameter. While the random factor can be hardly influenced, the decision parameter can be usually determined by a deterministic optimization problem depending on a corresponding probability measure. However, in applications the “underlying” probability measure is often a little different, replaced by empirical one determined on the base of data or even (for numerical reason) replaced by simpler...
On approximation in multistage stochastic programs: Markov dependence
A general multistage stochastic programming problem can be introduced as a finite system of parametric (one-stage) optimization problems with an inner type of dependence. Evidently, this type of the problems is rather complicated and, consequently, it can be mostly solved only approximately. The aim of the paper is to suggest some approximation solution schemes. To this end a restriction to the Markov type of dependence is supposed.
Thin and heavy tails in stochastic programming
Optimization problems depending on a probability measure correspond to many applications. These problems can be static (single-stage), dynamic with finite (multi-stage) or infinite horizon, single- or multi-objective. It is necessary to have complete knowledge of the “underlying” probability measure if we are to solve the above-mentioned problems with precision. However this assumption is very rarely fulfilled (in applications) and consequently, problems have to be solved mostly on the basis of...
Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric
Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall e. g., problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem of the utility functions. Especially, considering (where is a system of non decreasing concave nonnegative utility functions) we obtain...
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