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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 597 (24 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
A PRIMALDUAL TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION
, 2003
"... This paper concerns general (nonconvex) nonlinear optimization when first and second derivatives of the objective and constraint functions are available. The proposed method is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. T ..."
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Cited by 21 (3 self)
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This paper concerns general (nonconvex) nonlinear optimization when first and second derivatives of the objective and constraint functions are available. The proposed method is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penaltybarrier function that involves both primal and dual variables. Each subproblem is solved using a secondderivative Newtontype method that employs a combined trust region and line search strategy to ensure global convergence. It is shown that the trustregion step can be computed by factorizing a sequence of systems with diagonallymodified primaldual structure, where the inertia of these systems can be determined without recourse to a special factorization method. This has the benefit that offtheshelf linear system software can be used at all times, allowing the straightforward extension to largescale problems. Numerical results are given for problems in the COPS test collection.
InteriorPoint l_2Penalty Methods for Nonlinear Programming with Strong Global Convergence Properties
 Math. Programming
, 2004
"... We propose two line search primaldual interiorpoint methods that have a generic barrierSQP outer structure and approximately solve a sequence of equality constrained barrier subproblems. To enforce convergence for each subproblem, these methods use an # 2 exact penalty function eliminating the n ..."
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Cited by 9 (0 self)
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We propose two line search primaldual interiorpoint methods that have a generic barrierSQP outer structure and approximately solve a sequence of equality constrained barrier subproblems. To enforce convergence for each subproblem, these methods use an # 2 exact penalty function eliminating the need to drive the corresponding penalty parameter to infinity when finite multipliers exist. Instead of directly decreasing an equality constraint infeasibility measure, these methods attain feasibility by forcing this measure to zero whenever the steps generated by the methods tend to zero. Our analysis shows that under standard assumptions, our methods have strong global convergence properties. Specifically, we show that if the penalty parameter remains bounded, any limit point of the iterate sequence is either a KKT point of the barrier subproblem, or a FritzJohn (FJ) point of the original problem that fails to satisfy the MangasarianFromovitz constraint qualification (MFCQ); if the penalty parameter tends to infinity, there is a limit point that is either an infeasible FJ point of the inequality constrained feasibility problem (an infeasible stationary point of the infeasibility measure if slack variables are added) or a FJ point of the original problem at which the MFCQ fails to hold. Numerical results are given that illustrate these outcomes.