A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...

We show that Farkas’ lemma for linear inequality systems, established in 1902, continues to hold for separable sublinear inequality systems. As a consequence, we establish a qualification-free characterization of optimality for separable sublinear programming problems which include classes of robust linear programming problems.

The classical alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming problems and variational inequalities where both the involved operators and constraints are separable into two parts. In particular, recentness has witnessed a number of novel applications arising in diversified areas (e.g. Image Processing and Statistics), for which ...

An eecient numerical solution scheme entitled adaptive diierential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure. For a multiobjective control problem with a general separable structure, the \optimal" weighting coeecients for various performance indices are time-varying as the system evolves along any noninferior tr...

Introduction This paper describes the application of Newton Method for solving strictly convex separable network quadratic programs. The authors provide a brief synopsis of separable network quadratic programming and list the various techniques for solving the same. The main thrust of the paper is succinctly identified by the following: 1. Providing a generic subroutine that can be used by vari...