We introduce stochastic optimization problems involving stochastic dominance constraints. We develop necessary and sufficient conditions of optimality and duality theory for these models and show that the Lagrange mul...
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We introduce stochastic optimization problems involving stochastic dominance constraints. We develop necessary and sufficient conditions of optimality and duality theory for these models and show that the Lagrange multipliers corresponding to dominance constraints are concave nondecreasing utility functions. The models and results are illustrated on a portfolio optimization problem.
Different classes of nonconvex nonsmooth stochastic optimization problems are analyzed, their generalized differentiability properties and necessary optimality conditions are studied, and a technique for calculating s...
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Simultaneous perturbation stochastic approximation (SPSA) algorithms have been found to be very effective for high-dimensional simulation optimization problems. The main idea is to estimate the gradient using simulati...
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Simultaneous perturbation stochastic approximation (SPSA) algorithms have been found to be very effective for high-dimensional simulation optimization problems. The main idea is to estimate the gradient using simulation output performance measures at only two settings of the N -dimensional parameter vector being optimized rather than at the N + 1 or 2N settings required by the usual one-sided or symmetric difference estimates, respectively. The two settings of the parameter vector are obtained by simultaneously changing the parameter vector in each component direction using random perturbations. In this article, in order to enhance the convergence of these algorithms, we consider deterministic sequences of perturbations for two-timescale SPSA algorithms. Two constructions for the perturbation sequences are considered: complete lexicographical cycles and much shorter sequences based on normalized Hadamard matrices. Recently, one-simulation versions of SPSA have been proposed, and we also investigate these algorithms using deterministic sequences. Rigorous convergence analyses for all proposed algorithms are presented in detail. Extensive numerical experiments on a network of M/G/1 queues with feedback indicate that the deterministic sequence SPSA algorithms perform significantly better than the corresponding randomized algorithms.
In this article we discuss the application of a certain class of Monte Carlo methods to stochastic optimization problems. Particularly, we study variable-sample techniques, in which the objective function is replaced,...
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In this article we discuss the application of a certain class of Monte Carlo methods to stochastic optimization problems. Particularly, we study variable-sample techniques, in which the objective function is replaced, at each iteration, by a sample average approximation. We first provide general results on the schedule of sample sizes, under which variable-sample methods yield consistent estimators as well as bounds on the estimation error. Because the convergence analysis is performed pathwisely, we are able to obtain our results in a flexible setting, which requires mild assumptions on the distributions and which includes the possibility of using different sampling distributions along the algorithm. We illustrate these ideas by studying a modification of the well-known pure random search method, adapting it to the variable-sample scheme, and show conditions for convergence of the algorithm. Implementation issues are discussed and numerical results are presented to illustrate the ideas.
We consider structural topology optimization problems including unilateral constraints arising from, for example, nonpenetration conditions in contact mechanics or non-compression conditions for elastic ropes. To cons...
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We consider structural topology optimization problems including unilateral constraints arising from, for example, nonpenetration conditions in contact mechanics or non-compression conditions for elastic ropes. To construct more realistic models and to hedge off possible failures or an inefficient behaviour of optimal structures, we allow parameters (for example, loads) defining the problem to be stochastic. The resulting nonsmooth stochastic optimization problem is an instance of stochastic mathematical programs with equilibrium constraints (SMPEC), or stochastic bilevel programs. The existence as well as the continuity of optimal solutions with respect to the lower bounds on the design variables are established. The question of continuity of the optimal solutions with respect to small changes in the probability measure is analysed. For a subclass of the problems considered the answer is affirmative, thus establishing the robustness of optimal solutions.
We develop a stochastic programming model to aid manufacturing firms in making strategic decisions in technology acquisition. The proposed model maximizes the firm's expected profit under the condition of the unce...
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We develop a stochastic programming model to aid manufacturing firms in making strategic decisions in technology acquisition. The proposed model maximizes the firm's expected profit under the condition of the uncertainty in technological progress and development. To solve this large-scale problem, we decompose future uncertainties through scenarios and then develop an algorithm to solve the resulting non-linear subproblems efficiently. Finally, we develop a heuristic to eliminate the infeasibility in the master problem and obtain best solutions. Numerical results show that our heuristic solutions are very close to the optimal solutions and meaningful insights are derived.
In this paper, we consider the problem of hedging contingent claims on a stock under transaction costs and stochastic volatility. Extensive research has clearly demonstrated that the volatility of most stocks is not c...
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In this paper, we consider the problem of hedging contingent claims on a stock under transaction costs and stochastic volatility. Extensive research has clearly demonstrated that the volatility of most stocks is not constant over time. As small changes of the volatility can have a major impact on the value of contingent claims, hedging strategies should try to eliminate this volatility risk. We propose a stochastic optimization model for hedging contingent claims that takes into account the effects of stochastic volatility, transaction costs and trading restrictions. Simulation results show that our approach could improve performance considerably compared to traditional hedging strategies. (C) 2002 Published by Elsevier Science B.V.
Traditional models in multistage stochastic programming are directed to minimizing the expected value of random optimal costs arising in a multistage, non-anticipative decision process under uncertainty. Motivated by ...
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ISBN:
(纸本)1402075650
Traditional models in multistage stochastic programming are directed to minimizing the expected value of random optimal costs arising in a multistage, non-anticipative decision process under uncertainty. Motivated by risk aversion, we consider minimization of the probability that the random optimal costs exceed some preselected threshold value. For the two-stage case, we analyse structural properties and propose algorithms both for models with integer decisions and for those without. Extension of the modeling to the multistage situation concludes the paper.
The hybrid intelligent algorithm is often used to solve stochastic programming problems. In this paper, we propose the Particle Swarm Optimization (PSO) based hybrid intelligent algorithm. Preliminary experiment resul...
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ISBN:
(纸本)0780378652
The hybrid intelligent algorithm is often used to solve stochastic programming problems. In this paper, we propose the Particle Swarm Optimization (PSO) based hybrid intelligent algorithm. Preliminary experiment results suggest that this algorithm is feasible.
We address a stochastic single product manufacturing system in a make-to-stock environment with partial knowledge on future demand resulting from customers ordering in advance of their actual needs. The problem consis...
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