In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I 1 and I 4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well. Audience: Advanced undergraduate and graduate students, mathematical programming/ operations research specialists. Front Matter....Pages i-xix Preliminaries: Convex Analysis and Convex Programming....Pages 1-61 Front Matter....Pages 63-63 Introduction. Approximating the Separable Problem....Pages 65-77 Convex Separable Programming....Pages 79-90 Separable Programming: A Dynamic Programming Approach....Pages 91-139 Front Matter....Pages 141-141 Statement of the Main Problem. Basic Result....Pages 143-150 Version One: Linear Equality Constraints....Pages 151-158 The Algorithms....Pages 159-174 Version Two: Linear Constraint of the Form “≥”....Pages 175-180 Well-Posedness of Optimization Problems. On the Stability of the Set of Saddle Points of the Lagrangian....Pages 181-194 Extensions....Pages 195-206 Applications and Computational Experiments....Pages 207-222 Front Matter....Pages 227-227 Approximations with Respect to l 1 and l ∞ -Norms: An Application of Convex Separable Unconstrained Nondifferentiable Optimization....Pages 229-250 About Projections in the Implementation of Stochastic Quasigradient Methods to Some Probabilistic Inventory Control Problems. The Stochastic Problem of Best Chebyshev Approximation....Pages 251-262 Integrality of the Knapsack Polytope....Pages 263-266 Back Matter....Pages 269-316 "In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered. Convex separable programs subject to inequality/equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed." "As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I[subscript 1] and I[subscript [infinity]] norms, as a convex separable nonsmooth unconstrained minimization problem, is also considered." "Audience: Advanced undergraduate and graduate students, mathematical programming/operations research specialists."--BOOK JACKET In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered. Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed. As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well. __Audience:__ Advanced undergraduate and graduate students, mathematical programming/ operations research specialists.
