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17
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 ..."
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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.
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 115 (2 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 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...
Optimal Signal Sets For NonGaussian Detectors
 SIAM Journal on Optimization
, 1997
"... . Identifying a maximallyseparated set of signals is important in the design of modems. The notion of optimality is dependent on the model chosen to describe noise in the measurements; while some analytic results can be derived under the assumption of Gaussian noise, no such techniques are known fo ..."
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Cited by 9 (2 self)
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. Identifying a maximallyseparated set of signals is important in the design of modems. The notion of optimality is dependent on the model chosen to describe noise in the measurements; while some analytic results can be derived under the assumption of Gaussian noise, no such techniques are known for choosing signal sets in the nonGaussian case. To obtain numerical solutions for nonGaussian detectors, minimax problems are transformed into nonlinear programs, resulting in a novel formulation yielding problems with relatively few variables and many inequality constraints. Using sequential quadratic programming, optimal signal sets are obtained for a variety of noise distributions. Key words. Optimal Design, Inequality Constraints, Sequential Quadratic Programming Contribution of the National Institute of Standards and Technology and not subject to copyright in the United States. y Department of Mathematics, University of Michigan, Ann Arbor, MI 48109 z Mathematical and Computationa...
Methods for nonlinear constraints in optimization calculations
 THE STATE OF THE ART IN NUMERICAL ANALYSIS
, 1996
"... ..."
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.
Computational Experience of an InteriorPoint SQP Algorithm in a Parallel BranchandBound Framework
"... An interiorpoint algorithm within a parallel branchandbound framework for solving nonlinear mixed integer programs is described. The nonlinear programming relaxations at each node are solved using an interior point SQP method. In contrast to solving the relaxation to optimality at each tree node ..."
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Cited by 9 (3 self)
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An interiorpoint algorithm within a parallel branchandbound framework for solving nonlinear mixed integer programs is described. The nonlinear programming relaxations at each node are solved using an interior point SQP method. In contrast to solving the relaxation to optimality at each tree node, the relaxation is only solved to nearoptimality. Analogous to employing advanced bases in simplexbased linear MIP solvers, a “dynamic” collection of warmstart vectors is kept to provide “advanced warmstarts” at each branchandbound node. The code has the capability to run in both sharedmemory and distributedmemory parallel environments. Preliminary computational results on various classes of linear mixed integer programs and quadratic portfolio problems are presented.
On the Convergence Theory of TrustRegionBased Algorithms for EqualityConstrained Optimization
, 1995
"... In this paper we analyze incxact trust region interior point (TRIP) sequential quadr tic programming (SOP) 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 8 (0 self)
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In this paper we analyze incxact trust region interior point (TRIP) sequential quadr tic programming (SOP) 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 nonhnear constraints often come from the discretization of partial differential equations. In such cases the calculation of derivative information and the solution of hncarizcd equations is expensive. Often, the solution of hncar systems and derivatives arc computed incxactly yielding nonzero residuals. This paper
Sequential Quadratic Programming for LargeScale Nonlinear Optimization
 I⋅E I +w S⋅E S ES EI located Pareto optimum (a) (b) ZR E=w I⋅E I +w S⋅E S
, 1999
"... The sequential quadratic programming (SQP) algorithm has been one of the most successful general methods for solving nonlinear constrained optimization problems. We provide an introduction to the general method and show its relationship to recent developments in interiorpoint approaches. We emph ..."
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Cited by 5 (0 self)
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The sequential quadratic programming (SQP) algorithm has been one of the most successful general methods for solving nonlinear constrained optimization problems. We provide an introduction to the general method and show its relationship to recent developments in interiorpoint approaches. We emphasize largescale aspects. Key words: sequential quadratic programming, nonlinear optimization, Newton methods, interiorpoint methods, local convergence, global convergence ? Contribution of Sandia National Laboratories and not subject to copyright in the United States. Preprint submitted to Elsevier Preprint 1 July 1999 1 Introduction In this article we consider the general method of Sequential Quadratic Programming (hereafter denoted SQP) for solving the nonlinear programming problem minimize f(x) x subject to: h(x) = 0 g(x) 0 (NLP) where f : R n ! R, h : R n ! R m , and g : R n ! R p . Broadly defined, the SQP method is a procedure that generates iterates converging ...