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...

Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing. This problem is referred to as near-separable NMF and requires that there exists a cone spanned by a small subset of the columns of the input nonnegative ma...

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 propose a modification of our MPGP algorithm for the solution of bound constrained quadratic programming problems so that it can be used for minimization of a strictly convex quadratic function subject to separable convex constraints. Our active set based algorithm explores the faces by conjugate gradients and changes the active sets and active variables by gradient projections, possibly wit...

Theorems on the convex hull of an extended real-valued function living on a Hilbert space are presented in case the function is separable and in case the function is a composition of another function and a linear transformation. Equivalence of convex hulls of functions and their biconjugates is used. In particular, it is shown that under properness conditions the biconjugate of a separable func...

We consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition. These problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space. We fit an additively separable value function approximation using two techniques, namely, Lagrangian relaxation and the linear p...

We propose a new p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to linear programming problem with p-order conic constraints. We demonstrate that the developed model possesses excellent methodological and computational properties (e.g., it does not allow for a null separating hyperplane when the sets are linearly separable, etc). The ...

In this paper, by combining the splitting method of augmented Lagrange function (ALF) with sequential quadratic programming (SQP) approximation, a novel ALF-based algorithm SQP structure is proposed for multi-block linear constrained nonconvex separable optimization. The new uses idea to decompose original problem into several small-scale subproblems. Meanwhile, approximation and Armijo-type li...

In this paper, we describe a dynamic programming approach to find optimal trees to the singlesource minimum cost network flow problem with general nonlinear costs. This class of problems is known to be NP-Hard and there is a scarcity of methods to address them. The algorithms previously developed have considered only two particular types of cost functions: “staircase” and “sawtooth”. Here, a dy...