Stochastic ProgrammingStochastic programming - the science that provides us with tools to design and control stochastic systems with the aid of mathematical programming techniques - lies at the intersection of statistics and mathematical programming. The book Stochastic Programming is a comprehensive introduction to the field and its basic mathematical tools. While the mathematics is of a high level, the developed models offer powerful applications, as revealed by the large number of examples presented. The material ranges form basic linear programming to algorithmic solutions of sophisticated systems problems and applications in water resources and power systems, shipbuilding, inventory control, etc. Audience: Students and researchers who need to solve practical and theoretical problems in operations research, mathematics, statistics, engineering, economics, insurance, finance, biology and environmental protection. |
Contents
| 1 | |
Convex Polyhedra 35 | 34 |
Special Problems and Methods | 59 |
Logconcave and QuasiConcave Measures 87 | 86 |
Moment Problems | 125 |
Function | 146 |
Bounding and Approximation of Probabilities | 179 |
Statistical Decisions 219 | 218 |
Convexity Theory of Probabilistic Constrained Problems | 301 |
Programming under Probabilistic Constraint and Maximizing | 318 |
TwoStage Stochastic Programming Problems | 373 |
MultiStage Stochastic Programming Problems 425 | 424 |
Special Cases and Selected Applications | 447 |
Distribution Problems | 501 |
Appendix The Multivariate Normal Distribution | 541 |
| 589 | |
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Common terms and phrases
algorithm assume basic columns components compute concave concave function constraints in problem convex function convex polyhedron convex set corresponding covariance matrix defined designate deterministic Dirichlet distribution dual feasible basis dual method equal equation exists feasible solution finite number finite optimum formulated gamma distribution given go to Step hence implies integral interval Lemma lexicographic linear programming problem logconcave function lower bound maximization node nonlinear programming nonnegative normal distribution notations objective function obtain optimal solution optimum value possible values Prékopa primal feasible probabilistic constraint probability density function probability distribution function Proof prove random variables random vector respectively right hand side satisfying Section sequence simplex method solution of problem solve stochastic programming problem subject to Ax tableau Theorem upper bound upper principal value of problem μ₁ μο