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Journal ArticleDOI

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming

01 May 2006-Mathematical Programming (Springer-Verlag)-Vol. 106, Iss: 1, pp 25-57
TL;DR: A comprehensive description of the primal-dual interior-point algorithm with a filter line-search method for nonlinear programming is provided, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix.
Abstract: We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlinear programming.

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Citations
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Journal ArticleDOI
TL;DR: First the freefem++ software deals with mesh adaptation for problems in two and three dimension, second, it solves numerically a problem with phase change and natural convection, and finally to show the possibilities for HPC the software solves a Laplace equation by a Schwarz domain decomposition problem on parallel computer.
Abstract: This is a short presentation of the freefem++ software. In Section 1, we recall most of the characteristics of the software, In Section 2, we recall how to to build the weak form of a partial differential equation (PDE) from the strong form. In the 3 last sections, we present different examples and tools to illustrated the power of the software. First we deal with mesh adaptation for problems in two and three dimension, second, we solve numerically a problem with phase change and natural convection, and the finally to show the possibilities for HPC we solve a Laplace equation by a Schwarz domain decomposition problem on parallel computer.

2,867 citations

Journal ArticleDOI
TL;DR: This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.
Abstract: We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.

2,056 citations

Book
01 Dec 2004
TL;DR: This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.
Abstract: This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.

1,897 citations


Cites methods from "On the implementation of an interio..."

  • ...An excellent, open source implementation of the interior point algorithm is the code IPOPT (Wächter & Biegler, 2006)....

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Journal ArticleDOI
TL;DR: An overview, comparison and critical review of the different approaches to topology optimization, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
Abstract: Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.

1,816 citations

Journal ArticleDOI
TL;DR: A general-purpose MATLAB software program called GPOPS--II is described for solving multiple-phase optimal control problems using variable-order Gaussian quadrature collocation methods.
Abstract: A general-purpose MATLAB software program called GPOPS--II is described for solving multiple-phase optimal control problems using variable-order Gaussian quadrature collocation methods. The software employs a Legendre-Gauss-Radau quadrature orthogonal collocation method where the continuous-time optimal control problem is transcribed to a large sparse nonlinear programming problem (NLP). An adaptive mesh refinement method is implemented that determines the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy. The software can be interfaced with either quasi-Newton (first derivative) or Newton (second derivative) NLP solvers, and all derivatives required by the NLP solver are approximated using sparse finite-differencing of the optimal control problem functions. The key components of the software are described in detail and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a useful platform upon which to solve a wide variety of complex constrained optimal control problems.

1,074 citations

References
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Book
01 Nov 2008
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Abstract: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

17,420 citations

Book
01 Jan 2009
TL;DR: The aim of this book is to provide a Discussion of Constrained Optimization and its Applications to Linear Programming and Other Optimization Problems.
Abstract: Preface Table of Notation Part 1: Unconstrained Optimization Introduction Structure of Methods Newton-like Methods Conjugate Direction Methods Restricted Step Methods Sums of Squares and Nonlinear Equations Part 2: Constrained Optimization Introduction Linear Programming The Theory of Constrained Optimization Quadratic Programming General Linearly Constrained Optimization Nonlinear Programming Other Optimization Problems Non-Smooth Optimization References Subject Index.

7,278 citations


"On the implementation of an interio..." refers background in this paper

  • ..., [7, 12]) to improve the proposed step if a trial point has been rejected....

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  • ...Note that if the regularization parameter ζ > 0 is chosen sufficiently small, the optimization problem (30) is the exact penalty formulation [12] of the problem “find the feasible point that is closest (in a weighted norm) to the reference point x̄R ,”...

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Journal ArticleDOI
TL;DR: It is shown that performance profiles combine the best features of other tools for performance evaluation to create a single tool for benchmarking and comparing optimization software.
Abstract: We propose performance profiles — distribution functions for a performance metric — as a tool for benchmarking and comparing optimization software. We show that performance profiles combine the best features of other tools for performance evaluation.

3,729 citations


"On the implementation of an interio..." refers methods in this paper

  • ...For the comparisons in the next sections we make use of the Dolan-Moré performance profiles [9]....

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  • ...4 The problems with altered problem size are CATENARY, CHARDIS1, CONT5-QP, CONT6-QQ, CVXQP1, CVXQP2, CVXQP3, DRCAV1LQ, DRCAV2LQ, DRCAV3LQ, DRCAVTY3, EG3, EIGENA, EIGENALS, EIGENB, EIGENB2, EIGENBCO, EIGENBLS, EIGENC, EIGENC2, EIGENCCO, EIGENCLS, FLOSP2HH, FLOSP2HL, FLOSP2HM, FMINSURF, GAUSSELM, HARKERP2, LUBRIF, LUBRIFC, NCVXQP[1-9], NONCVXU2, NONMSQRT, POWER, SCURLY30, SPARSINE, SPARSQUR....

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  • ...Furthermore, IPOPT aborted in 3 problems because it reverted to the restoration phase when the constraint violation was already below the termina- 4 The problems with altered problem size are CATENARY, CHARDIS1, CONT5-QP, CONT6-QQ, CVXQP1, CVXQP2, CVXQP3, DRCAV1LQ, DRCAV2LQ, DRCAV3LQ, DRCAVTY3, EG3, EIGENA, EIGENALS, EIGENB, EIGENB2, EIGENBCO, EIGENBLS, EIGENC, EIGENC2, EIGENCCO, EIGENCLS, FLOSP2HH, FLOSP2HL, FLOSP2HM, FMINSURF, GAUSSELM, HARKERP2, LUBRIF, LUBRIFC, NCVXQP[1-9], NONCVXU2, NONMSQRT, POWER, SCURLY30, SPARSINE, SPARSQUR....

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Book
01 Jan 1968
TL;DR: This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere.
Abstract: : This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere. It provides a fresh presentation of nonlinear programming theory, a detailed review of other unconstrained methods, and a development of the latest algorithms for unconstrained minimization. (Author)

2,493 citations