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16
Snopt: An SQP Algorithm For LargeScale Constrained Optimization
, 1997
"... 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 ..."
Abstract

Cited by 332 (18 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.
A Sqp Method For General Nonlinear Programs Using Only Equality Constrained Subproblems
 MATHEMATICAL PROGRAMMING
, 1993
"... In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [34] it is much simpler to implement and allows any kind of changes of the working s ..."
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Cited by 48 (2 self)
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In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [34] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SQPmethods, as demonstrated by extensive numerical tests.
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 35 (8 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...
A reduced Hessian method for largescale constrained optimization
 SIAM JOURNAL ON OPTIMIZATION
, 1995
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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 26 (2 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 ...
A Global Convergence Analysis Of An Algorithm For Large Scale Nonlinear Optimization Problems
, 1996
"... . In this paper we give a global convergence analysis of a basic version of an SQP algorithm described in [2] for the solution of large scale nonlinear inequalityconstrained optimization problems. Several procedures and options have been added to the basic algorithm to improve the practical perform ..."
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Cited by 14 (4 self)
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. In this paper we give a global convergence analysis of a basic version of an SQP algorithm described in [2] for the solution of large scale nonlinear inequalityconstrained optimization problems. Several procedures and options have been added to the basic algorithm to improve the practical performance; some of these are also analyzed. The important features of the algorithm include the use of a constrained merit function to assess the progress of the iterates and a sequence of approximate merit functions that are less expensive to evaluate. It also employs an interior point quadratic programming solver that can be terminated early to produce a truncated step. Key words. Sequential Quadratic Programming, Global Convergence, Merit Function, Large Scale Problems. AMS subject classifications. 49M37, 65K05, 90C30 1. Introduction. In this report we consider an algorithm to solve the inequalityconstrained minimization problem, min x f(x) subject to: g(x) 0; (1.1) where x 2 R n , and...
Analysis of Inexact TrustRegion InteriorPoint SQP Algorithms
, 1995
"... In this paper we analyze inexact trustregion interiorpoint (TRIP) sequential quadratic programming (SQP) algorithms for the solution of optimization problems with nonlinear equality constraints and simple bound constraints on some of the variables. Such problems arise in many engineering applicati ..."
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Cited by 11 (7 self)
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In this paper we analyze inexact trustregion interiorpoint (TRIP) sequential quadratic programming (SQP) algorithms for the solution of optimization problems with nonlinear equality constraints and simple bound constraints on some of the variables. Such problems arise in many engineering applications, in particular in optimal control problems with bounds on the control. The nonlinear constraints often come from the discretization of partial differential equations. In such cases the calculation of derivative information and the solution of linearized equations is expensive. Often, the solution of linear systems and derivatives are computed inexactly yielding nonzero residuals. This paper analyzes the effect of the inexactness onto the convergence of TRIP SQP and gives practical rules to control the size of the residuals of these inexact calculations. It is shown that if the size of the residuals is of the order of both the size of the constraints and the trustregion radius, t...
Methods for nonlinear constraints in optimization calculations
 THE STATE OF THE ART IN NUMERICAL ANALYSIS
, 1996
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SQP methods for largescale nonlinear programming
, 1999
"... We compare and contrast a number of recent sequential quadratic programming (SQP) methods that have been proposed for the solution of largescale nonlinear programming problems. Both linesearch and trustregion approaches are considered, as are the implications of interiorpoint and quadratic progr ..."
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Cited by 9 (0 self)
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We compare and contrast a number of recent sequential quadratic programming (SQP) methods that have been proposed for the solution of largescale nonlinear programming problems. Both linesearch and trustregion approaches are considered, as are the implications of interiorpoint and quadratic programming methods.
Some Reflections on the Current State of ActiveSet and InteriorPoint Methods for Constrained Optimization
, 2003
"... We reect on the current state of activeset and interiorpoint methods for convex and nonconvex constrained optimization. We voice some concerns about current SQP methods. ..."
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Cited by 3 (1 self)
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We reect on the current state of activeset and interiorpoint methods for convex and nonconvex constrained optimization. We voice some concerns about current SQP methods.