optimization problems in which the random variables are represented by an extremely large number of scenarios. The method involves the binarization of the probability distribution, and the generation of a consistent partially defined Boolean function (pdBf) representing the combination (F,p) of the binarized probability distribution F and the enforced probability level p. We show that … Read more
This paper presents a two stage stochastic equilibrium problem with equilibrium constraints(SEPEC) model. Some source problems which motivate the model are discussed. Monte Carlo sampling method is applied to solve the SEPEC. The convergence analysis on the statistical estimators of Nash equilibria and Nash stationary points are presented. Article Download View Two stage stochastic equilibrium … Read more
We investigate sample average approximation of a general class of one-stage stochastic mathematical programs with equilibrium constraints. By using graphical convergence of unbounded set-valued mappings, we demonstrate almost sure convergence of a sequence of stationary points of sample average approximation problems to their true counterparts as the sample size increases. In particular we show the … Read more
A.D.Roy’s (1952) safety first (SF) approach to a financial portfolio selection is improved. Safety first means minimization of probability of poor returns. Improvement concerns a better estimation of the poor return probabilities by means of shortfall risk functions. Optimal SF-portfolio is sought similar to Roy’s geometric method but with a different efficient frontier. In case … Read more
In this paper we present a generic algorithmic framework, namely, the accelerated stochastic approximation (AC-SA) algorithm, for solving strongly convex stochastic composite optimization (SCO) problems. While the classical stochastic approximation (SA) algorithms are asymptotically optimal for solving differentiable and strongly convex problems, the AC-SA algorithm, when employed with proper stepsize policies, can achieve optimal or … Read more
This paper describes how to incorporate stochastic curvature information in a Newton- CG method and in a limited memory quasi-Newton method for large scale optimization. The motivation for this work stems from statistical learning and stochastic optimization applications in which the objective function is the sum of a very large number of loss terms, and … Read more
The deregulation of electricity markets increases the financial risk faced by retailers who procure electric energy on the spot market to meet their customers’ electricity demand. To hedge against this exposure, retailers often hold a portfolio of electricity derivative contracts. In this paper, we propose a multistage stochastic mean-variance optimisation model for the management of … Read more
The paper studies large scale mixed integer reformulation approach to stochastic programming problems containing probability and quantile functions, under assumption of discreteness of the probability distribution involved. Jointly with general sample approximation technique and contemporary mixed integer programming solvers the approach gives a regular framework to solution of practical probabilistic programming problems. In the literature … Read more
Dentcheva and Ruszczynski recently proposed using a stochastic dominance constraint to specify risk preferences in a stochastic program. Such a constraint requires the random outcome resulting from one’s decision to stochastically dominate a given random comparator. These ideas have been extended to problems with multiple random outcomes, using the notion of positive linear stochastic dominance. … Read more
Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based, treelike parallelization with interior-point methods and a Schur complement mechanism. However, the direct linear solves involving the Schur complement matrix are expensive, and adversely a ect the scalability of this approach. In this paper we propose a stochastic preconditioner to address … Read more