Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

An efficient 3D topology optimization code written in Matlab

Abstract: This paper presents an efficient and compact Matlab code to solve three-dimensional topology optimization problems. The 169 lines comprising this code include finite element analysis, sensitivity analysis, density filter, optimality criterion optimizer, and display of results. The basic code solves minimum compliance problems. A systematic approach is presented to easily modify the definition of supports and external loads. The paper also includes instructions to define multiple load cases, active and passive elements, continuation strategy, synthesis of compliant mechanisms, and heat conduction problems, as well as the theoretical and numerical elements to implement general non-linear programming strategies such as SQP and MMA. The code is intended for students and newcomers in the topology optimization. The complete code is provided in Appendix C and it can be downloaded from http://top3dapp.com .

Sensitivity analysis for nonlinear programming using penalty methods

Abstract: In this paper we establish a theoretical basis for utilizing a penalty-function method to estimate sensitivity information (i.e., the partial derivatives) of a localsolution and its associated Lagrange multipliers of a large class of nonlinear programming problems with respect to a general parametric variation in the problem functions. The local solution is assumed to satisfy the second order sufficient conditions for a strict minimum. Although theoretically valid for higher order derivatives, the analysis concentrates on the estimation of the first order (first partial derivative) sensitivity information, which can be explicitly expressed in terms of the problem functions. For greater clarity, the results are given in terms of the mixed logarithmic-barrier quadratic-loss function. However, the approach is clearly applicable toany algorithm that generates a once differentiable "solution trajectory".

Lagrange programming neural networks

Abstract: A class of neural networks appropriate for general nonlinear programming, i.e., problems including both equality and inequality constraints, is analyzed in detail. The methodology is based on the Lagrange multiplier theory in optimization and seeks to provide solutions satisfying the necessary conditions of optimality. The equilibrium point of the network satisfies the Kuhn-Tucker condition for the problem. No explicit restriction is imposed on the form of the cost function apart from some general regularity and convexity conditions. The stability of the neural networks is analyzed in detail. The transient behavior of the network is simulated and the validity of the approach is verified for a practical problem, maximum entropy image restoration. >

An interior point nonlinear programming for optimal power flow problems with a novel data structure

Abstract: This paper presents a new interior point nonlinear programming algorithm for optimal power flow problems (OPF) based on the perturbed KKT conditions of the primal problem. Through the concept of the centering direction, the authors extend this algorithm to classical power flow (PF) and approximate OPF problems. For the latter, CPU time can be reduced substantially. To efficiently handle functional inequality constraints, a reduced correction equation is derived, the size of which depends on that of equality constraints. A novel data structure is proposed which has been realized by rearranging the correction equation. Compared with the conventional data structure of Newton OPF, the number of fill-ins of the proposed scheme is roughly halved and CPU time is reduced by about 15% for large scale systems. The proposed algorithm includes four kinds of objective functions and two different data structures. Extensive numerical simulations on test systems that range in size from 14 to 1047 buses, have shown that the proposed method is very promising for large scale application due to its robustness and fast execution time.

Linear and Nonlinear Programming

Abstract: This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve a problem. This was a major theme of the first edition of this book and the fourth edition expands and further illustrates this relationship. As in the earlier editions, the material in this fourth edition is organized into three separate parts. Part I is a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities.New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming. Indeed, many conic structures are possible and useful in a variety of applications. It must be recognized, however, that conic linear programming is an advanced topic, requiring special study. Another important topic is an accelerated steepest descent method that exhibits superior convergence properties, and for this reason, has become quite popular. The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8. As in previous editions, end-of-chapter exercises appear for all chapters.From the reviews of the Third Edition: this very well-written book is a classic textbook in Optimization. It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn. (Jean-Jacques Strodiot, Zentralblatt MATH, Vol. 1207, 2011)