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13
A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
 SIAM Journal on Optimization
, 2001
"... . A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the pr ..."
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Cited by 23 (0 self)
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. A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast local convergence properties. A preliminary implementation has been tested and some promising numerical results are reported. Key words. sequential quadratic programming, SQP, feasible iterates, feasible SQP, FSQP AMS subject classifications. 49M37, 65K05, 65K10, 90C30, 90C53 PII. S1052623498344562 1.
Convergence Criteria for Hierarchical Overlapping Coordination of Linearly Constrained Convex Problems
 Computational Optimization and Applications
, 1998
"... Decomposition of multidisciplinary engineering system design problems into smaller subproblems is desirable because it enhances robustness and understanding of the numerical results. Subproblems can be solved in parallel using the optimization technique most suitable for the underlying mathematical ..."
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Cited by 6 (5 self)
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Decomposition of multidisciplinary engineering system design problems into smaller subproblems is desirable because it enhances robustness and understanding of the numerical results. Subproblems can be solved in parallel using the optimization technique most suitable for the underlying mathematical form of the subproblem. Hierarchical overlapping coordination (HOC) is an interesting strategy for solving decomposed problems. It simultaneously uses two or more design problem decompositions, each of them associated with different partitions of the design variables and constraints. Coordination is achieved by the exchange of information between decompositions. This article presents the HOC algorithm and several new sufficient conditions for convergence of the algorithm to the optimum in the case of convex problems with linear constraints. One of these equivalent conditions involves the rank of the constraint matrix that is computationally efficienttoverify. Computational results obtained b...
An NE/SQP Method for the Bounded Nonlinear Complementarity Problem
 Preprint MCSP5080495, Argonne National Laboratory, Argonne
, 1995
"... NE/SQP is a recent algorithm that has proven quite effective for solving the pure and mixed forms of the nonlinear complementarity problem (NCP). NE/SQP is robust in the sense that its directionfinding subproblems are always solvable; in addition, the convergence rate of this method is Qquadratic. ..."
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Cited by 1 (1 self)
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NE/SQP is a recent algorithm that has proven quite effective for solving the pure and mixed forms of the nonlinear complementarity problem (NCP). NE/SQP is robust in the sense that its directionfinding subproblems are always solvable; in addition, the convergence rate of this method is Qquadratic. In this paper we consider a generalized version of NE/SQP proposed by Pang and Qi, that is suitable for the bounded NCP. We extend their work by demonstrating a stronger convergence result and then test a proposed method on several numerical problems. Key Words: Nonlinear complementarity problem, mathematical programming, sequential quadratic programming. 1 Introduction In a recent paper [18] Pang and Qi presented a general algorithm to solve various mathematical programs that can be formulated as systems of nonsmooth equations. Various convergence results were shown for several general nonsmooth formulations. One specific nonsmooth system considered was the upper bounded nonlinear compl...
User’s Guide for SQOPT Version 7: Software for LargeScale Linear and Quadratic Programming ∗
, 2008
"... SQOPT is a software package for minimizing a convex quadratic function subject to both equality and inequality constraints. SQOPT may also be used for linear programming and for finding a feasible point for a set of linear equalities and inequalities. SQOPT uses a twophase, activeset, reduceHessi ..."
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SQOPT is a software package for minimizing a convex quadratic function subject to both equality and inequality constraints. SQOPT may also be used for linear programming and for finding a feasible point for a set of linear equalities and inequalities. SQOPT uses a twophase, activeset, reduceHessian method. It is most efficient on problems with relatively few degrees of freedom (for example, if only some of the variables appear in the quadratic term, or the number of active constraints and bounds is nearly as large as the number of variables). However, unlike previous versions of SQOPT, there is no limit on the number of degrees of freedom. SQOPT is primarily intended for large linear and quadratic problems with sparse constraint matrices. A quadratic term 1 2 xTHx in the objective function is represented by a user subroutine that returns the product Hx for a given vector x. SQOPT uses stable numerical methods throughout and includes a reliable basis package (for maintaining sparse LU factors of the basis matrix), a practical antidegeneracy procedure, scaling, and elastic bounds on any number of constraints and variables. SQOPT is part of the SNOPT package for largescale nonlinearly constrained optimization. The source code is reentrant and suitable for any machine with a Fortran compiler (or the f2c translator and a C compiler). SQOPT may be called from a driver program in Fortran, C, or Matlab. It can also be used as a standalone package, reading data in the MPS format used by commercial mathematical programming systems.
A SECOND DERIVATIVE SQP METHOD: THEORETICAL ISSUES ∗
, 2008
"... Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exactHessian SQP methods. In particul ..."
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Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exactHessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a secondderivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descentconstraint is imposed on certain QP subproblems, which “guides ” the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established. Key words. Nonlinear programming, nonlinear inequality constraints, sequential quadratic programming, ℓ1penalty function, nonsmooth optimization
Complementary Condensing for the Direct Multiple Shooting Method
"... Summary. In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretiz ..."
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Summary. In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning the solution of the quadratic subproblems we present a factorization of the QP’s KKT system, based on a combined null–space range–space approach exploiting the problem’s block sparse structure. We demonstrate the merit of this approach for a vehicle control problem in which the integer gear decision is convexified. 1
A SECOND DERIVATIVE SQP METHOD: THEORETICAL ISSUES ∗
, 2008
"... Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exactHessian SQP methods. In particul ..."
Abstract
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Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exactHessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a secondderivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descentconstraint is imposed on certain QP subproblems, which “guides ” the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established. Key words. Nonlinear programming, nonlinear inequality constraints, sequential quadratic programming, ℓ1penalty function, nonsmooth optimization
A SECOND DERIVATIVE SQP METHOD WITH IMPOSED DESCENT ∗
, 2008
"... Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exactHessian SQP methods. In particul ..."
Abstract
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Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exactHessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a secondderivative Sℓ1QP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent constraint is imposed on certain QP subproblems, which “guides ” the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established. Key words. Nonlinear programming, nonlinear inequality constraints, sequential quadratic programming, ℓ1 penalty function, nonsmooth optimization