We consider the problem of minimizing a convex linear-fractional separable function over a feasible region defined by a convex inequality constraint or linear inequality constraint, and bounds on the variables (box constraints). These problems are interesting from both theoretical and practical points of view because they arise in somemathematical programming problems and in various practical p...

We study the modeling of non-convex piecewise linear functions as Mixed Integer Programming (MIP) problems. We review several new and existing MIP formulations for continuous piecewise linear functions with special attention paid to multivariate non-separable functions. We compare these formulations with respect to their theoretical properties and their relative computational performance. In ad...

The wavelet transform is denoted by ‘WT’ gained wide-ranging approval in processing signal and in compressing image. A 2D analysis must be implemented to use WT for processing the image. Such powerful signal analysis technique can be implemented for non-stationary data using Lifting architecture for the Discrete Wavelet Transform (DWT). Since high speed implementation with low latency is a dema...

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...

Broadly, we study continuous games (those with continuous strategy spaces and utility functions) with a view towards computation of equilibria. We cover all of the gametheoretic background needed to understand these results in detail. Then we present new work, which can be divided into three parts. First, it is known that arbitrary continuous games may have arbitrarily complicated equilibria, s...

We consider a general class of dynamic programming (DP) problems with nonseparable objective functions. show that for any problem in this class, there exists an augmented-state DP satisfies the principle optimality and solutions to which yield original problem. Furthermore, we identify subclass naturally forward separable functions state-augmentation scheme is tractable. extend framework stocha...

The standard Dynamic Programming (DP) formulation can be used to solve Multi-Stage Optimization Problems (MSOP’s) with additively separable objective functions. In this paper we consider a larger class of MSOP’s monotonically backward functions; functions being special case We propose necessary and sufficient condition, utilizing generalization Bellman’s equation, for solution MSOP, cost functi...

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...