R. Conn, N.I.M. Gould, Ph.L. Toint, "Large-scale nonlinear constrained optimization: a current survey", in Algorithms for continuous optimization: the state of the art, 434, Kluwer Academic, (ed.) E. Spedicato, pp. 287-332, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... and have been implemented in sophisticated software MINOS [55] LANCELOT [19] SNOPT [34] Filter SQP [28] LOQO [78] CONOPT [23] LAGRG2 [71] NPSOL [32] NLPQL [69] SPRNLP [5] 6] TRIP [21] BETR [64] GINO [44] For a survey of nonlinear optimization methods and software, see [53] and [16]. Many of these codes are capable of solving a large array of problems [37] and can take advantage of sparsity in the objective function and constraints. The algorithms implemented in these successful implementations belong to one of the following four categories: Sequential quadratic programming ....

A.R. Conn, N. Gould, and Ph.L. Toint. Large-scale nonlinear constrained optimization: A current survey. In D.F. Shanno L. Dixon and E. Spedicato, editors, Algorithms for Continuous Optimization: State of the Art. Kluwer Academic Publishers, 1994.

....submitting to the power of advanced algorithmic development and of modern computing environments, leading to the formulation of models requiring solutions of these problems in a variety of scientific areas. Two excellent recent reviews are given by Coleman (Coleman, 1992) and Conn, Gould and Toint (Conn et al. 1992), who survey some important applications as well as recent trends in algorithms and consider the impact of parallel computing architectures for large scale optimization. Following these authors we take the term large scale to mean any optimization problem that is large enough so that the ....

Conn, A. R., Gould, N. I. M., Toint, Ph. T., (1992) " Large-scale nonlinear constrained optimization.

....to use the modified barrier function method of Polyak [23] During each iteration Polyak s method solves an unconstrained problem with two parameters. This method is shown to be superior to the classic barrier methods. Some comments and modifications of Polyak s method can be found in Conn et al. [5], Breitfeld and Shanno [1] and [2] The advantage of using the modified barrier function method for (CP) is the following: the corresponding logarithmic barrier function for the kth iteration is just an unconstrained DTOC problem: CPB) min M (k) P N Gamma1 i=1 (L i (y i ; x i ) Gamma ....

A. R. Conn, N. I. M. Gould, and Ph. L. Toint. Large-scale nonlinear constrained optimization: a current survey. Technical Report TR/PA/94/03, CERFACS, France, 1994.

....in Section 6 we briefly consider weaknesses in the current version of the algorithm and suggest possible avenues of research that will improve its efficiency. For a discussion of the theoretical and practical questions related to large scale nonlinear programming see the recent surveys [Col] and [CGT92b]. 2. An Interior Point QP Solver Interior point methods for linear programming have been demonstrated to be very successful, especially on large problems, and recent research has lead to their extension to quadratic programs. A particular method, the method of optimizing over low dimensional ....

A. R. Conn, N. I. M. Gould, and Ph. T. Toint. Large-scale nonlinear constrained optimization. Technical Report 92-02, Facult'es Universitaires de Namur, D'epartement de Math'ematique, 1992.

....control theory, physics, engineering. The goal of this paper is to give an overview on nonlinear optimization both on the theory as on practical methods, putting an emphasis on algorithms. There are already several textbooks and surveys about this field, like [1] 7] 10] 23] 38] 3] [4]. All of them contain some theory and numerical methods. What is new here is the attempt to present all classes of methods used for solving optimization problems: numeric, interval or symbolic. This survey does not pretend to give a full and complete presentation of all optimization algorithms, ....

....of unconstrained problems derived from the original one. Furthermore, a multidimensional minimization problem is reduced to a sequence of univariate minimizations (sometimes called line minimizations or line searches) Good textbooks on numerical methods are: 1] 7] 10] For surveys, see [4], 3] Algorithms and implementations for the unconstrained case, can be found in [26] 4.1 Univariate minimization Let a; b 2 R. Suppose that the function f : R R has a minimum point in [a; b] The interval [a; b] is called interval of uncertainty. What one wants is to make this interval as ....

A. R. Conn, N. I. M. Gould, and Ph. L. Toint. Large-scale nonlinear constrained optimization: a current survey. Technical Report TR/PA/94/03, CERFACS, Toulouse, France, 94.

....the use of conjugate gradients with various preconditioners. These include ffl diagonal preconditioners, ffl band preconditioners, ffl incomplete Cholesky preconditioners, ffl expanding band preconditioners, and ffl full matrix factorization preconditioners. Further details are given in Conn, Gould and Toint, 1992. We have decided to explore other alternatives, keeping in mind that the preconditioners should take advantage of the structure of the problems given by the partial separability and that we must be able to control their inertia. Thus, in this paper, we study the use of the following ....

A. R. Conn, N. I. M. Gould, and Ph. L. Toint. Large-scale nonlinear constrained optimization. In J. R. E. O'Malley, ed., `Proceedings of the Second International Conference on Industrial and Applied Mathematics', pp. 51--70, SIAM, Philadelphia, USA, 1992.

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R. Conn, N.I.M. Gould, Ph.L. Toint, "Large-scale nonlinear constrained optimization: a current survey", in Algorithms for continuous optimization: the state of the art, 434, Kluwer Academic, (ed.) E. Spedicato, pp. 287-332, 1994.

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