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46
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 582 (23 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
Sequential Quadratic Programming
, 1995
"... this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can ..."
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Cited by 162 (4 self)
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this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can
A trust region method based on interior point techniques for nonlinear programming
 Mathematical Programming
, 1996
"... Jorge Nocedal z An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described. It applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direc ..."
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Cited by 152 (19 self)
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Jorge Nocedal z An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described. It applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives. This framework permits primal and primaldual steps, but the paper focuses on the primal version of the new algorithm. An analysis of the convergence properties of this method is presented. Key words: constrained optimization, interior point method, largescale optimization, nonlinear programming, primal method, primaldual method, SQP iteration, barrier method, trust region method.
CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2001
"... The initial release of CUTE, a widely used testing environment for optimization software was described in [2]. The latest version, now known as CUTEr is presented. New features include reorganisation of the environment to allow simultaneous multiplatform installation, new tools for, and interface ..."
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Cited by 86 (8 self)
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The initial release of CUTE, a widely used testing environment for optimization software was described in [2]. The latest version, now known as CUTEr is presented. New features include reorganisation of the environment to allow simultaneous multiplatform installation, new tools for, and interfaces to, optimization packages, and a considerably simplified and entirely automated installation procedure for unix systems. The SIF decoder, which used to be a part of CUTE, has become a separate tool, easily callable by various packages. It features simple extensions to the SIF test problem format and the generation of files suited to automatic differentiation packages.
On the solution of equality constrained quadratic programming problems arising . . .
, 1998
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TrustRegion InteriorPoint Algorithms For Minimization Problems With Simple Bounds
 SIAM J. CONTROL AND OPTIMIZATION
, 1995
"... Two trustregion interiorpoint algorithms for the solution of minimization problems with simple bounds are analyzed and tested. The algorithms scale the local model in a way similar to Coleman and Li [1]. The first algorithm is more usual in that the trust region and the local quadratic model are c ..."
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Cited by 56 (18 self)
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Two trustregion interiorpoint algorithms for the solution of minimization problems with simple bounds are analyzed and tested. The algorithms scale the local model in a way similar to Coleman and Li [1]. The first algorithm is more usual in that the trust region and the local quadratic model are consistently scaled. The second algorithm proposed here uses an unscaled trust region. A global convergence result for these algorithms is given and dogleg and conjugategradient algorithms to compute trial steps are introduced. Some numerical examples that show the advantages of the second algorithm are presented.
TrustRegion InteriorPoint SQP Algorithms For A Class Of Nonlinear Programming Problems
 SIAM J. CONTROL OPTIM
, 1997
"... In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal co ..."
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Cited by 46 (9 self)
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In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints, but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed for a different class of problems by Coleman and Li and they exploit trustregion techniques for equalityconstrained optimizatio...
Global Convergence of TrustRegion SQPFilter Algorithms for General Nonlinear Programming
, 1999
"... Global convergence to firstorder critical points is proved for two trustregion SQPfilter algorithms of the type introduced by Fletcher and Leyffer (1997). The algorithms allow for an approximate solution of the quadratic subproblem and incorporate the safeguarding tests described in Fletcher, Ley ..."
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Cited by 41 (5 self)
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Global convergence to firstorder critical points is proved for two trustregion SQPfilter algorithms of the type introduced by Fletcher and Leyffer (1997). The algorithms allow for an approximate solution of the quadratic subproblem and incorporate the safeguarding tests described in Fletcher, Leyffer and Toint (1998). The first algorithm decomposes the step into its normal and tangential components, while the second replaces this decomposition by a stronger condition on the associated model decrease. 1 Department of Mathematics, University of Dundee, Dundee, DD1 4HN, Scotland, EU. Email : fletcher@mcs.dundee.ac.uk, sleyffer@mcs.dundee.ac.uk 2 Current reports available from "http://www.mcs.dundee.ac.uk:8080/~dfg/Narep.html". 3 Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 0QX, England, EU. Email : n.gould@rl.ac.uk 4 Current reports available from "http://www.numerical.rl.ac.uk/reports/reports.html". 5 Department ...
InexactRestoration Algorithm for Constrained Optimization
 Journal of Optimization Theory and Applications
, 1999
"... We introduce a new model algorithm for solving nonlinear programming problems. No slack variables are introduced for dealing with inequality constraints. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved and in second phase the ob ..."
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Cited by 27 (6 self)
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We introduce a new model algorithm for solving nonlinear programming problems. No slack variables are introduced for dealing with inequality constraints. Each iteration of the method proceeds in two phases. In the first phase, feasibility of the current iterate is improved and in second phase the objective function value is reduced in an approximate feasible set. The point that results from the second phase is compared with the current point using a nonsmooth merit function that combines feasibility and optimality. This merit function includes a penalty parameter that changes between different iterations. A suitable updating procedure for this penalty parameter is included by means of which it can be increased or decreased along different iterations. The conditions for feasibility improvement at the first phase and for optimality improvement at the second phase are mild, and largescale implementations of the resulting method are possible. We prove that under suitable conditions, that ...