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LOQO: An interior point code for quadratic programming
, 1994
"... ABSTRACT. This paper describes a software package, called LOQO, which implements a primaldual interiorpoint method for general nonlinear programming. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programming with only brief mention of the extensions to convex ..."
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Cited by 156 (9 self)
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ABSTRACT. This paper describes a software package, called LOQO, which implements a primaldual interiorpoint method for general nonlinear programming. We focus in this paper mainly on the algorithm as it applies to linear and quadratic programming with only brief mention of the extensions to convex and general nonlinear programming, since a detailed paper describing these extensions were published recently elsewhere. In particular, we emphasize the importance of establishing and maintaining symmetric quasidefiniteness of the reduced KKT system. We show that the industry standard MPS format can be nicely formulated in such a way to provide quasidefiniteness. Computational results are included for a variety of linear and quadratic programming problems. 1.
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 114 (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 Practical Algorithm For General Large Scale Nonlinear Optimization Problems
 SIAM Journal on Optimization
, 1994
"... . We provide an effective and efficient implementation of a sequential quadratic programming (SQP) algorithm for the general large scale nonlinear programming problem. In this algorithm the quadratic programming subproblems are solved by an interior point method that can be prematurely halted by a t ..."
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Cited by 22 (10 self)
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. We provide an effective and efficient implementation of a sequential quadratic programming (SQP) algorithm for the general large scale nonlinear programming problem. In this algorithm the quadratic programming subproblems are solved by an interior point method that can be prematurely halted by a trust region constraint. Numerous computational enhancements to improve the numerical performance are presented. These include a dynamic procedure for adjusting the merit function parameter and procedures for adjusting the trust region radius. Numerical results and comparisons are presented. Key words: nonlinear programming, interior point, SQP, merit function, trust region, large scale 1. Introduction. In a series of recent papers, [3], [6], and [8], the authors have developed a new algorithmic approach for solving large, nonlinear, constrained optimization problems. This proposed procedure is, in essence, a sequential quadratic programming (SQP) method that uses an interior point algorithm...
A Truncated SQP Algorithm for Large Scale Nonlinear Programming Problems
 Advances in Optimization and Numerical Analysis: Proceedings of the Sixth Workshop on Optimization and Numerical Analysis
"... We consider the inequality constrained nonlinear programming problem and an SQP algorithm for its solution. We are primarily concerned with two aspects of the general procedure, namely, the approximate solution of the quadratic program, and the need for an appropriate merit function. We first descri ..."
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Cited by 5 (3 self)
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We consider the inequality constrained nonlinear programming problem and an SQP algorithm for its solution. We are primarily concerned with two aspects of the general procedure, namely, the approximate solution of the quadratic program, and the need for an appropriate merit function. We first describe an (iterative) interiorpoint method for the quadratic programming subproblem that, no matter when it is terminated, yields a descent direction for a suggested new merit function. An algorithm based on ideas from trustregion and truncated Newton methods is suggested and some of our preliminary numerical results are discussed.
An InteriorPoint Method for General LargeScale Quadratic Programming Problems
 Annals of Operations Research
, 1996
"... In this paper we present an interior point algorithm for solving both convex and nonconvex quadratic programs. The method, which is an extension of our interior point work on linear programming problems, efficiently solves a wide class of large scale problems and forms the basis for a sequential qua ..."
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Cited by 1 (0 self)
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In this paper we present an interior point algorithm for solving both convex and nonconvex quadratic programs. The method, which is an extension of our interior point work on linear programming problems, efficiently solves a wide class of large scale problems and forms the basis for a sequential quadratic programming (SQP) solver for general large scale nonlinear programs. The key to the algorithm is a 3dimensional costimprovement subproblem, which is solved at every iteration. We have developed an approximate recentering procedure and a novel, adaptive bigM Phase I procedure that are essential to the success. We describe the basic method along with the recentering and bigM Phase I procedures. Details of the implementation and computational results are also presented. Keywords: bigM Phase I procedure, convex quadratic programming, interior point methods, linear programming, method of centers, multidirectional search direction, nonconvex quadratic programming, recentering. # Cont...
Solving Multistage Stochastic Programs With Tree Dissection
, 1991
"... One component of every multistage stochastic program is a filtration that determines the notion of which random events are observable at each stage of the evolution. Within the context of interiorpoint methods, we describe an efficient preordering technique, called filtered dissection, that takes ..."
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One component of every multistage stochastic program is a filtration that determines the notion of which random events are observable at each stage of the evolution. Within the context of interiorpoint methods, we describe an efficient preordering technique, called filtered dissection, that takes advantage of the filtration's structure to dramatically reduce fillin in the factorization as compared with methods such as the default methods employed by cplexbarrier and loqo. We have implemented this technique as a minor modification to loqo, and it produces a roughly 200fold performance improvement. In particular, we have solved a previouslyunsolvable, realworld, 6stage financial investment problem having 800K equations and 1,200K variables (and 8,192 points in its sample space) using a single processor SGI workstation. The filtered dissection algorithm applies in a natural manner to generic (linear and convex) multistage stochastic programs. The approach promises to eliminate t...
Solving Multistage Stochastic Programs With
, 1991
"... One componentofevery multistage stochastic program is a #ltration that determines the notion of which random events are observable at each stage of the evolution. Within the context of interiorpoint methods, we describe an e#cient preordering technique, called #ltered dissection, that takes a ..."
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One componentofevery multistage stochastic program is a #ltration that determines the notion of which random events are observable at each stage of the evolution. Within the context of interiorpoint methods, we describe an e#cient preordering technique, called #ltered dissection, that takes advantage of the #ltration's structure to dramatically reduce #llin in the factorization as compared with methods such as the default methods employed by cplexbarrier and loqo.Wehave implemented this technique as a minor modi#cation to loqo, and it produces a roughly 200fold performance improvement. In particular, wehave solved a previouslyunsolvable, realworld, 6stage #nancial investment problem having 800K equations and 1,200K variables #and 8,192 points in its sample space# using a single processor SGI workstation.