# STOCHASTIC PROGRAMS WITH RECOURSE

@article{Walkup1967STOCHASTICPW, title={STOCHASTIC PROGRAMS WITH RECOURSE}, author={David W. Walkup and Roger J.-B. Wets}, journal={Siam Journal on Applied Mathematics}, year={1967}, volume={15}, pages={1299-1314} }

Abstract : So far the study of stochastic programs with recourse has been limited to the case (called by G. Dantzig programming under uncertainty) when only the right-hand sides or resources of the problem are random. In this paper the authors extend the theory to the general case when essentially all the parameters involved are random. This generalization immediately raises the problem of attributing a precise meaning to the stochastic constraints. They examine a probability formulation…

## 173 Citations

### Recourse-based stochastic nonlinear programming: properties and Benders-SQP algorithms

- Mathematics, Computer ScienceComput. Optim. Appl.
- 2012

A novel hybrid algorithm that combines sequential quadratic programming (SQP) and Benders decomposition is presented and obtained Lagrange multiplier estimates in this framework poses a unique challenge and are shown to be cheaply obtainable through the solution of a single low-dimensional QP.

### Stochastic Programs with Fixed Recourse: The Equivalent Deterministic Program

- Mathematics
- 1974

To each stochastic program corresponds an equivalent deterministic program. The purpose of this paper is to compile and extend the known properties for the equivalent deterministic program of a…

### Stochastic Programs with Recourse: Random Recourse Costs Only

- Mathematics
- 1973

In this paper we discuss the class of stochastic programs with recourse in which the only randomness present is in the recourse costs. Two economic interpretations are given. We present results which…

### STOCHASTIC LINEAR PROGRAMMING WITH RECOURSE: A TUTORIAL*

- Computer Science
- 1980

The algorithm for solving stochastic linear programs with simple recourse may be particularly interesting since Wets shows in that paper how the problem can be reduced to an equivalent deterministic linear program of the same dimensionality.

### SOLUTION THEOREMS IN PROBABILISTIC PROGRAMMING: A LINEAR PROGRAMMING APPROACH.

- Computer Science
- 1967

### The value of the stochastic solution in stochastic linear programs with fixed recourse

- Computer ScienceMath. Program.
- 1982

Borders on the value of the stochastic solution are presented, that is, the potential benefit from solving the stoChastic program over solving a deterministic program in which expected values have replaced random parameters.

### Two-Stage Stochastic Semidefinite Programming: Theory, Algorithms, and Application to AC Power Flow under Uncertainty

- Computer Science
- 2016

This thesis considers risk neutral and risk averse two-stage stochastic semidefinite programs with continuous and mixed-integer recourse, respectively, and applies their structure, solution methods relying on decomposition, and results to unit commitment in alternating current (AC) power systems.

### Computational Algorithms for Convex Stochastic Programs with Simple Recourse

- MathematicsOper. Res.
- 1970

The algorithms presented apply when the preference functions h(x) and g(y) are convex, and continuously differentiable, k is a convex polytope, ξ has a distribution that satisfies mild convergence conditions, and the objective is to minimize the expectation of the sum of the two preference functions.

### Multistage stochastic programs: The state-of-the-art and selected bibliography

- EconomicsKybernetika
- 1995

The traditional deterministic optimization models are limited in practical applications because the models parameters (future demands, interest rates, water inflows, resources, etc.) are not completely known when some decision is needed.

## References

SHOWING 1-10 OF 51 REFERENCES

### STOCHASTIC PROGRAMS WITH RECOURSE: SPECIAL FORMS,

- Computer Science
- 1967

Some special forms of stochastic programs with recourse are considered, which, because they are less general, may prove to be more amenable to computational solution.

### Stochastic Programs with Recourse II: On the Continuity of the Objective

- Mathematics
- 1969

Abstract : In an earlier paper, 'Stochastic Programs with Recourse,' the authors introduced a general class of stochastic (linear) programs and showed, among other things, that the objective of any…

### A Stochastic Transportation Problem

- Mathematics
- 1963

When the market demands for a commodity are not known with certainty, the problem of scheduling shipments to a number of demand points from several supply points is a stochastic transportation…

### On Some Theorems of Stochastic Linear Programming with Applications

- Mathematics
- 1963

A linear programming problem is said to be stochastic if one or more of the coefficients in the objective function or the system of constraints or resource availabilities is known only by its…

### Programming Under Uncertainty: The Equivalent Convex Program

- Mathematics
- 1966

This paper is an attempt to describe and characterize the equivalent convex program of a two-stage linear program under uncertainty. The study has been divided into two parts. In the first one, we…

### Inequalities for Stochastic Linear Programming Problems

- Mathematics
- 1960

Consider a linear-programming problem in which the “right-hand side” is a random vector whose expected value is known and where the expected value of the objective function is to be minimized. An…

### Two-Stage Programming under Uncertainty with Discrete Distribution Function

- EconomicsOper. Res.
- 1967

This paper establishes the relation between two approaches for solving two-stage programming under uncertainty with discrete distribution function using optimality conditions and a simple change in variables and introduces a stochastic Leontief production model.

### ON THE SOLUTION OF TWO-STAGE LINEAR PROGRAMS UNDER UNCERTAINTY. NOTES ON LINEAR PROGRAMMING AND EXTENSIONS. PART 55

- Mathematics
- 1961

This analysis investigates the conditions under which the first-stage decisions are optimal, and formulas for using various existing computational algorithms to obtain an optimal solution are given.

### ON MINIMIZING A CONVEX FUNCTION SUBJECT TO LINEAR INEQUALITIES

- Mathematics
- 1955

SUMMARY THE minimization of a convex function of variables subject to linear inequalities is discussed briefly in general terms. Dantzig's Simplex Method is extended to yield finite algorithms for…