E-convex function was introduced by Youness 1 and revised by Yang 2 . Chen 3 introduced Semi-E-convex function and studied some of its properties. Syau and Lee 4 defined E-quasi-convex function, strictly E-quasi-convex function and studied some basic properties. Fulga and Preda 5 introduced the class of E-preinvex and E-prequasi-invex functions. All the above E-convex and generalized E-convex f...

The orthogonal packing of rectangular items in an arbitrary convex region is considered in this work. The packing problem is modeled as the problem of deciding for the feasibility or infeasibility of a set of nonlinear equality and inequality constraints. A procedure based on nonlinear programming is introduced and numerical experiments which show that the new procedure is reliable are exhibite...

ABSTRACT. This paper describes a software package, called LOQO, which implements a primaldual interior-point method for general nonlinear programming. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programming with only brief mention of the extensions to convex and general nonlinear programming, since a detailed paper describing these extensions were publis...

Convex optimization techniques are widely used in the design and analysis of communication systems and signal processing algorithms. In this paper a novel recurrent neural network is presented for solving nonlinear strongly convex equality constrained optimization problems. The proposed neural network is based on recursive quadratic programming for nonlinear optimization, in conjunction with ho...

In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for solving them in which each iteration is obtained by solving a convex programming problem. Under some suitable assumptions, we establish that any accumulation poi...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

Global exponential stability is a desirable property for dynamic systems. This paper studies the global exponential stability of several existing recurrent neural networks for solving linear programming problems, convex programming problems with interval constraints, convex programming problems with nonlinear constraints, and monotone variational inequalities. In contrast to the existing result...

A convex body K in R has associated with it a unique circumscribed ellipsoid CE(K) with minimum volume, and a unique inscribed ellipsoid IE(K) with maximum volume. We first give a unified, modern exposition of the basic theory of these extremal ellipsoids using the semi–infinite programming approach pioneered by Fritz John in his seminal 1948 paper. We then investigate the automorphism groups o...

Optimization is a procedure of finding and comparing feasible solutions until no better solution can be found. It can be divided into several fields, one of which is the Convex Optimization. It is characterized by a convex objective function and convex constraint functions over a convex set which is the set of the decision variables. This can be viewed, on the one hand, as a particular case of ...

A wide variety of stability and performance problems for linear and certain classes of nonlinear dynamical systems can be formulated as convex optimization problems involving linear matrix inequalities (LMIs). These formulations can be solved numerically with computationally-efficient interior-point methods. Many of the first LMI-based stability formulations applied to linear systems and the cl...