Journal ArticleDOI
Contributions to the theory of stochastic programming
TLDR
The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures on two stochastic programming decision models, where the solvability of the second stage problem only with a prescribed (high) probability is required.Abstract:
Two stochastic programming decision models are presented. In the first one, we use probabilistic constraints, and constraints involving conditional expectations further incorporate penalties into the objective. The probabilistic constraint prescribes a lower bound for the probability of simultaneous occurrence of events, the number of which can be infinite in which case stochastic processes are involved. The second one is a variant of the model: two-stage programming under uncertainty, where we require the solvability of the second stage problem only with a prescribed (high) probability. The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures.read more
Citations
More filters
Journal ArticleDOI
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality
Marco C. Campi,Simone Garatti +1 more
TL;DR: It is proved that, if constraints in the SP problem are optimally removed—i.e., one deletes those constraints leading to the largest possible cost improvement—, then a precise optimality link to the original chance-constrained problem CCP in addition holds.
Journal ArticleDOI
Asymptotic behavior of statistical estimators and of optimal solutions of stochastic optimization problems
Jitka Dupačová,Roger J.-B. Wets +1 more
TL;DR: In this paper, the authors studied the asymptotic behavior of the statistical estimators that maximize a not necessarily dieren tiable criterion function, possibly subject to side constraints (equalities and inequalities).
Journal ArticleDOI
Concavity and Efficient Points of Discrete Distributions in Probabilistic Programming
TL;DR: The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations and the concept of r-concave discrete probability distributions is introduced.
Journal ArticleDOI
An Introductory Tutorial on Stochastic Linear Programming Models
Suvrajeet Sen,Julia L. Higle +1 more
TL;DR: This work discusses a variety of LP-based models that can be used for planning under uncertainty, and presents models that range from simple recourse policies to more general two-stage and multistage SLP formulations.
Journal ArticleDOI
On mixing sets arising in chance-constrained programming
TL;DR: A compact extended reformulation that characterizes a linear programming equivalent of a single chance constraint with equal scenario probabilities and a compact extended linear program for the intersection of multiple mixing sets and a cardinality constraint for a special case is given.
References
More filters
Book
Nonlinear Programming: Sequential Unconstrained Minimization Techniques
TL;DR: This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere.
Journal ArticleDOI
Linear Programming under Uncertainty
TL;DR: This article originally appeared in Management Science, April-July 1955, Volume 1, Numbers 3 and 4, pp. 197-206, published by The Institute of Management Sciences.
Journal ArticleDOI
Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating Oil
TL;DR: In this paper, an integrated series of operations research studies directed toward improvement in such scheduling methods is presented. But the focus is on essentials of the mathematical model and other phases of the OR studies are brought in only as required.
Journal ArticleDOI
On minimizing a convex function subject to linear inequalities
TL;DR: In this paper, the Simplex Method was extended to yield finite algorithms for minimizing either a convex quadratic function or the sum of the t largest of a set of linear functions and the solution of a generalization of the latter problem is indicated.