Allan D. Waren

Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming

Abstract : The purpose of this paper is to describe a Generalized Reduced Gradient (GRG) algorithm for nonlinear programming, its implementation as a FORTRAN program for solving small to medium size problems, and some computational results. Our focus is more on the software implementation of the algorithm than on its mathematical properties. This is in line with the premise that robust, efficient, easy to use NLP software must be written and made accessible if nonlinear programming is to progress, both in theory and in practice.

Design and Use of the Microsoft Excel Solver

In designing the spreadsheet optimizer that is bundled with Microsoft Excel, we and Microsoft made certain choices in designing its user interface, model processing, and solution algorithms for linear, nonlinear, and integer programs. We describe some of the common pitfalls users encounter and remedies available in the latest version of Microsoft Excel. The Solver has many applications and great impact in industry and education.

The Status of Nonlinear Programming Software

Desirable features of software for solving nonlinear optimization problems are discussed, and several available codes for solving NLPs are described in terms of these features. Codes are classified by algorithm type. Addresses where codes may be obtained are given. The paper concludes with a brief survey of available computational experience with several classes of algorithms and with some of the specific codes considered.

User-oriented criteria for the selection of DSS software

Both the composition of the selection team and the choice of evaluation criteria should reflect the end-user orientation of DSS software.

Feature Article—Survey of Nonlinear Programming Applications

Several factors imply an increase in the use of nonlinear optimization models. We face serious problems of declining productivity and increasingly scarce, expensive raw materials. Computers are becoming cheaper and faster, and more efficient nonlinear programming (NLP) algorithms are being developed. This paper attempts to illustrate the potential of NLP by describing the application of nonlinear programming models to three classes of problems: petrochemical industry applications, nonlinear networks, and economic planning. Problems in the petrochemical industry ranging from product blending, refinery unit optimization, and unit design to multiplant production, and distribution planning are discussed. The nonlinear networks topic includes electric power dispatch, hydroelectric reservoir management, and problems involving traffic flow in urban transportation networks. In economic planning, we describe NLP applications involving large dynamic econometric models, a variety of static equilibrium models, and su...

Optimization in engineering design

It is shown that many engineering design problems can be formulated in terms of inequality constraints on the system response function(s) and on the design parameters. Any set of design variables for which these constraints are satisfied constitutes an acceptable design. There may be many acceptable designs or none at all. In either case it is possible to define a best or optimal design in a meaningful minimax sense. Such an optimal design is the solution of a related nonlinear programming problem involving the minimization of an easily determined objective function, subject to inequality constraints. Some suggested minimization techniques for solving such problems are briefly described. Two reasonably complex examples, using these methods, are presented: the first details the design of an under-water sonar system and the second describes the design of a wideband crystal filter.

The status of nonlinear programming software: an update

This paper reports on progress in nonlinear programming software since 1979. Developments in the computer industry have had a significant impact on the design of mathematical software and the expectations of users. Microcomputers in particular are changing the software industry to an extent that was not anticipated in the last survey. Continuing refinements in NLP algorithms have enabled users to solve larger and more complicated problems, even some with integer variables. Modeling systems with nonlinear programming capabilities have now become available. Interest and improvements in computational experimentation have increased the rigor and objectivity of studies assessing software quality. This report surveys these important developments and speculates on the future.

Large scale nonlinear programming

Abstract Our ability to solve large nonlinear programs has increased significantly in the last several years. New algorithms have been developed, existing ones have been refined, some good software has been developed, and there has been some computational experience and practical applications. This paper summarizes some of this activity, focusing on Successive Linear Programming (SLP), Successive Quadratic Programming (SQP), and Generalized Reduced Gradient (GRG) algorithims.

Optimal Design of Filters with Bounded, Lossy Elements

This paper proposes a solution to the problem of designing a filter of given structure, incorporating nonideal elements, to meet or exceed given insertion loss specifications subject to element value bounds. This problem is reformulated as a nonlinear programming problem, i.e., minimize an objective function subject to inequality constraints, whose solution yields a filter optimal in a min-max sense. To solve this problem, a recent penalty function approach is used, which converts the constrained problem into a sequence of unconstrained minimizations. These minimizations are carried out using a recent, very efficient, descent technique. The overall method is especially amenable to computer implementation. These techniques have been applied to the computer design of cascade crystal-realizable lattice filters. The results for several designs are presented, and are uniformly good.

GRG2: an all FORTRAN general purpose nonlinear optimizer

GRG2 solves nonlinear optimization problems in which the objective and constraint functions can have nonlinearities of any form but should be differentiable. Both single and double precision versions are available for computers of all major vendors.