The paper considers a quadratic programming problem with strictly convex separable objective function, single linear constraint, and two-sided constraints on variables. This is commonly called the Convex Knapsack Separable Quadratic Problem, or CKSQP for short. We are interested in an algorithm solving time complexity. papers devoted to this topic contain inaccuracies description of algorithms ...

The aim of this manuscript is to approach by means first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (...

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...

Manufacturing scheduling is an important but difficult task. Building on our previous success in developing optimization-based scheduling methods using Lagrangian relaxation for practical applications, this paper presents a novel Lagrangian relaxation neural network (LRNN) optimization techniques. The convergence of LRNN for separable convex programming problems is established. For separable in...

In this paper, we propose a new branch and bound algorithm for the solution of large scale separable concave programming problems. The largest distance bisection (LDB) technique is proposed to divide rectangle into sub-rectangles when one problem is branched into two subproblems. It is proved that the LDB method is a normal rectangle subdivision(NRS). Numerical tests on problems with dimensions...

Conventional methods of solving nonconvex separable programming (NSP) problems by mixed integer programming methods requires adding numerous 0±1 variables. In this work, we present a new method of deriving the global optimum of a NSP program using less number of 0±1 variables. A separable function is initially expressed by a piecewise linear function with summation of absolute terms. Linearizin...

In this paper we address the problem of frequency stability in unit commitment (UC) optimisation process. We include a set appropriately defined constraints UC formulation for operational planning scenarios advance real-time operation. Consequently, cover system against loss largest infeed under N−1 security criterion.The main contribution our work consists using method separable programming to...

We consider the separable quadratic multi-knapsack problem (QMKP) which consists in maximizing a concave separable quadratic integer function subject to m linear capacity constraints. The aim of this paper is to develop an effective method to compute an upper bound for (QMKP) from a surrogate relaxation originally proposed in Djerdjour et al. (1988). The quality of three other upper bounds for...

Abstract In this paper, we present an inexact multiblock alternating direction method for the point-contact friction model of force-optimization problem (FOP). The friction-cone constraints FOP are reformulated as Cartesian product circular cones. We focus on convex quadratic circular-cone programming FOP, which is exact cone-programming model. Coupled with separable objective function, recast ...