Results 1  10
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23
Newton's Method For Large BoundConstrained Optimization Problems
 SIAM JOURNAL ON OPTIMIZATION
, 1998
"... We analyze a trust region version of Newton's method for boundconstrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearlyconstrained problems, and yields global and superlinea ..."
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Cited by 74 (4 self)
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We analyze a trust region version of Newton's method for boundconstrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearlyconstrained problems, and yields global and superlinear convergence without assuming neither strict complementarity nor linear independence of the active constraints. We also show that the convergence theory leads to an efficient implementation for large boundconstrained problems.
Global Convergence of a Class of Trust Region Algorithms for Optimization Using Inexact Projections on Convex Constraints
, 1995
"... A class of trust region based algorithms is presented for the solution of nonlinear optimization problems with a convex feasible set. At variance with previously published analysis of this type, the theory presented allows for the use of general norms. Furthermore, the proposed algorithms do not r ..."
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Cited by 51 (4 self)
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A class of trust region based algorithms is presented for the solution of nonlinear optimization problems with a convex feasible set. At variance with previously published analysis of this type, the theory presented allows for the use of general norms. Furthermore, the proposed algorithms do not require the explicit computation of the projected gradient, and can therefore be adapted to cases where the projection onto the feasible domain may be expensive to calculate. Strong global convergence results are derived for the class. It is also shown that the set of linear and nonlinear constraints that are binding at the solution are identified by the algorithms of the class in a finite number of iterations.
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 new active set algorithm for box constrained Optimization
 SIAM Journal on Optimization
, 2006
"... Abstract. An active set algorithm (ASA) for box constrained optimization is developed. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for branching between the two steps. Global convergence to a stationary point is established ..."
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Cited by 26 (6 self)
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Abstract. An active set algorithm (ASA) for box constrained optimization is developed. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for branching between the two steps. Global convergence to a stationary point is established. For a nondegenerate stationary point, the algorithm eventually reduces to unconstrained optimization without restarts. Similarly, for a degenerate stationary point, where the strong secondorder sufficient optimality condition holds, the algorithm eventually reduces to unconstrained optimization without restarts. A specific implementation of the ASA is given which exploits the recently developed cyclic Barzilai–Borwein (CBB) algorithm for the gradient projection step and the recently developed conjugate gradient algorithm CG DESCENT for unconstrained optimization. Numerical experiments are presented using box constrained problems in the CUTEr and MINPACK2 test problem libraries. Key words. nonmonotone gradient projection, box constrained optimization, active set algorithm,
TrustRegion Proper Orthogonal Decomposition for Flow Control
 Institute for Computer
, 2000
"... . The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial di#erential equations, e.g. fluid flows. It can also be used to develop reduced order control models. The essential is the computation of POD basis functions that r ..."
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Cited by 24 (2 self)
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. The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial di#erential equations, e.g. fluid flows. It can also be used to develop reduced order control models. The essential is the computation of POD basis functions that represent the influence of the control action on the system in order to get a suitable control model. We present an approach where the suitable reduced order model is derived successively and give global convergence results. Keywords: proper orthogonal decomposition, flow control, reduced order modeling, trust region methods, global convergence 1. Introduction. We present a robust reduced order method for the control of complex timedependent physical processes governed by partial di#erential equations (PDE). Such a control problem often is hard to solve because of the high order system that describes the state (a large number of (finite element) basis elements for every point in the time d...
SurrogateAssisted Evolutionary Optimization Frameworks for HighFidelity Engineering Design Problems
 In Knowledge Incorporation in Evolutionary Computation
, 2004
"... Over the last decade, Evolutionary Algorithms (EAs) have emerged as a powerful paradigm for global optimization of multimodal functions. More recently, there has been significant interest in applying EAs to engineering design problems. However, in many complex engineering design problems where high ..."
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Cited by 16 (4 self)
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Over the last decade, Evolutionary Algorithms (EAs) have emerged as a powerful paradigm for global optimization of multimodal functions. More recently, there has been significant interest in applying EAs to engineering design problems. However, in many complex engineering design problems where highfidelity analysis models are used, each function evaluation may require a Computational Structural Mechanics (CSM), Computational Fluid Dynamics (CFD) or Computational ElectroMagnetics (CEM) simulation costing minutes to hours of supercomputer time. Since EAs typically require thousands of function evaluations to locate a near optimal solution, the use of EAs often becomes computationally prohibitive for this class of problems. In this paper, we present frameworks that employ surrogate models for solving computationally expensive optimization problems on a limited computational budget. In particular, the key factors responsible for the success of these frameworks are discussed. Experimental results obtained on benchmark test functions and realworld complex design problems are presented.
On Iterative Algorithms for Linear Least Squares Problems With Bound Constraints
, 1995
"... Three new iterative methods for the solution of the linear least squares problem with bound constraints are presented and their performance analyzed. The first is a modification of a method proposed by Lotstedt, while the two others are characterized by a technique allowing for fast active set chang ..."
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Cited by 15 (2 self)
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Three new iterative methods for the solution of the linear least squares problem with bound constraints are presented and their performance analyzed. The first is a modification of a method proposed by Lotstedt, while the two others are characterized by a technique allowing for fast active set changes resulting in noticeable improvements on the speed at which constraints active at the solution are identified. The numerical efficiency of these algorithms is experimentally studied, with particular emphasis on dependence of the starting point choice and the use of preconditioning for illconditioned problems.
NonMonotone TrustRegion Methods for BoundConstrained Semismooth Equations with Applications to Nonlinear Mixed Complementarity Problems
, 1999
"... We develop and analyze a class of trustregion methods for boundconstrained semismooth systems of equations. The algorithm is based on a simply constrained differentiable minimization reformulation. Our global convergence results are developed in a very general setting that allows for nonmonotoni ..."
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Cited by 14 (4 self)
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We develop and analyze a class of trustregion methods for boundconstrained semismooth systems of equations. The algorithm is based on a simply constrained differentiable minimization reformulation. Our global convergence results are developed in a very general setting that allows for nonmonotonicity of the function values at subsequent iterates. We propose a way of computing trial steps by a semismooth Newtonlike method that is augmented by a projection onto the feasible set. Under a DennisMoretype condition we prove that close to a BDregular solution the trustregion algorithm turns into this projected Newton method, which is shown to converge locally qsuperlinearly or quadratically, respectively, depending on the quality of the approximate BDsubdifferentials used. As an important application we discuss in detail how the developed algorithm can be used to solve nonlinear mixed complementarity problems (MCPs). Hereby, the MCP is converted into a boundconstrained semismooth...
An iterative workingset method for LargeScale NonConvex quadratic programming
, 2001
"... We consider a workingset method for solving largescale quadratic programming problems for which there is no requirement that the objective function be convex. The methods are iterative at two levels, one level relating to the selection of the current working set, and the second due to the method u ..."
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Cited by 6 (1 self)
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We consider a workingset method for solving largescale quadratic programming problems for which there is no requirement that the objective function be convex. The methods are iterative at two levels, one level relating to the selection of the current working set, and the second due to the method used to solve the equalityconstrained problem for this working set. A preconditioned conjugate gradient method is used for this inner iteration, with the preconditioner chosen especially to ensure feasibility of the iterates. The preconditioner is updated at the conclusion of each outer iteration to ensure that this feasibility requirement persists. The wellknown equivalence between the conjugategradient and Lanczos methods is exploited when nding directions of negative curvature. Details of an implementation  the Fortran 90 package QPA in the forthcoming GALAHAD library  are given.