Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. Despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...

Automized stabilization and control of computer-controlled nonlinear processes is considered. A new algorithm which constitutes a combination of Popov's and of Jury and Lee's stability criteria with a nonlinear programming approach is proposed. The algorithm is applied to a digitally controlled antenna tracking system and the operation is simulated on an IBM 360/91 computer. The solution involv...

This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integ...

An exact semidefinite linear programming (SDP) relaxation of a nonlinear semidefinite programming problem is a highly desirable feature because a semidefinite linear programming problem can efficiently be solved. This paper addresses the basic issue of which nonlinear semidefinite programming problems possess exact SDP relaxations under a constraint qualification. We do this by establishing exa...

This work is an example of application of nonlinear programming to a problem of three-dimensional trajectory optimization for multistage launch vehicles for geostationary orbit missions. The main objective is to minimize fuel consumption or equivalently to maximize the payload. The launch vehicle considered here, Europa-II, consists of 5 thrust phases and 2 coast phases. Major parameters of the...

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear...

Recently, the area of Mixed Integer Nonlinear Programming (MINLP) has experienced tremendous growth and a flourish of research activity. In this article we will give a brief overview of past developments in the MINLP arena and discuss some of the future work that can foster the development of MINLP in general and, in particular, robust solver technology for the practical solution of problems.

Shortcomings of the conventional problem format in nonlinear programming suggest the need for a broader model that features composite terms. Such a model, promoting better representation of the problem structures found in applications, can be adopted with no real sacrifice in computing practicality.

In this paper are defined new firstand second-order duals of the nonlinear programming problem with inequality constraints. We introduce a notion of a WD-invex problem. We prove weak, strong, converse, strict converse duality, and other theorems under the hypothesis that the problem is WD-invex. We obtain that a problem with inequality constraints is WD-invex if and only if weak duality holds b...