Separable Optimization: Theory and Methods

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

Stefan M. Stefanov is a Professor in the Department of Mathematics, South-West University ＂Neofit Rilski,＂ Blagoevgrad, Bulgaria. He is author of several books, and journal and conference papers. His interests are in the areas of optimization (separable, convex, stochastic, nondifferentiable, nonlinear), operations research, numerical analysis, approximation theory, inequalities.