In this paper we are interested in the convergence analysis of the Stochastic Dual Dynamic Algorithm (SDDP) algorithm in a general framework, and regardless of whether the underlying probability space is discrete or not. We consider a convex stochastic control program not necessarily linear and the resulting dynamic programming equation. We prove under mild assumptions … Read more
In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the latter to a convex and differentiable function with Lipschitz continuous gradient by using both variable and constant smoothing parameters. … Read more
In this paper, we study self-avoiding walks of a given length on a graph. We consider a formulation of this problem as a binary linear program. We analyze the polyhedral structure of the underlying polytope and describe valid inequalities. Proofs for their facial properties for certain special cases are given. In a variation of this … Read more
Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on … Read more
This paper is concerned with tuning the Stochastic Dual Dynamic Programming algorithm to make it more computationally efficient. We report the results of some computational experiments on a large-scale hydrothermal scheduling model developed for Brazil. We find that the best improvements in computation time are obtained from an implementation that increases the number of scenarios … Read more
We discuss conditions for the Aubin property of solutions to perturbed cone constrained programs, by using and refining results given in \cite{KlaKum02}. In particular, we show that constraint nondegeneracy and hence uniqueness of the multiplier is necessary for the Aubin property of the critical point map. Moreover, we give conditions under which the critical point … Read more
We develop the concept of utility robustness to address the problem of ambiguity and inconsistency in utility assessments. A robust decision-making framework is built on a utility set which characterizes a decision maker’s risk attitude described by boundary and auxiliary conditions. This framework is studied using the Sample Average Approximation (SAA) approach. We show the … Read more
Chance constrained programming is an effective and convenient approach to control risk in decision making under uncertainty. However, due to unknown probability distributions of random parameters, the solution obtained from a chance constrained optimization problem can be biased. In practice, instead of knowing the true distribution of a random parameter, only a series of historical … Read more
In 2001, info-gap decision theory re-invented the then 40-year old model of local robustness, known universally as radius of stability (circa 1960). Since then, this model of local robustness has been promoted by info-gap scholars as a reliable tool for the management of a severe uncertainty that is characterized by a vast (e.g. unbounded) uncertainty … Read more
We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs, Proc. IPCO 2010, Lecture Notes in Computer Science, vol. 6080, Springer, 2010, pp. 219–229], … Read more