Results 1  10
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74
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 166 (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.
Implementation of interior point methods for large scale linear programming
 Interior Point Methods in Mathematical Programming
, 1996
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Solving LargeScale Linear Programs by InteriorPoint Methods Under the MATLAB Environment
 Optimization Methods and Software
, 1996
"... In this paper, we describe our implementation of a primaldual infeasibleinteriorpoint algorithm for largescale linear programming under the MATLAB 1 environment. The resulting software is called LIPSOL  Linearprogramming InteriorPoint SOLvers. LIPSOL is designed to take the advantages of M ..."
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Cited by 63 (1 self)
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In this paper, we describe our implementation of a primaldual infeasibleinteriorpoint algorithm for largescale linear programming under the MATLAB 1 environment. The resulting software is called LIPSOL  Linearprogramming InteriorPoint SOLvers. LIPSOL is designed to take the advantages of MATLAB's sparsematrix functions and external interface facilities, and of existing Fortran sparse Cholesky codes. Under the MATLAB environment, LIPSOL inherits a high degree of simplicity and versatility in comparison to its counterparts in Fortran or C language. More importantly, our extensive computational results demonstrate that LIPSOL also attains an impressive performance comparable with that of efficient Fortran or C codes in solving largescale problems. In addition, we discuss in detail a technique for overcoming numerical instability in Cholesky factorization at the endstage of iterations in interiorpoint algorithms. Keywords: Linear programming, PrimalDual infeasibleinteriorp...
Symmetric quasidefinite matrices
 SIAM Journal on Optimization
, 1995
"... We say that a symmetric matrix K is quasidefinite if it has the form ..."
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Cited by 62 (3 self)
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We say that a symmetric matrix K is quasidefinite if it has the form
Algorithms For Complementarity Problems And Generalized Equations
, 1995
"... Recent improvements in the capabilities of complementarity solvers have led to an increased interest in using the complementarity problem framework to address practical problems arising in mathematical programming, economics, engineering, and the sciences. As a result, increasingly more difficult pr ..."
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Cited by 45 (5 self)
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Recent improvements in the capabilities of complementarity solvers have led to an increased interest in using the complementarity problem framework to address practical problems arising in mathematical programming, economics, engineering, and the sciences. As a result, increasingly more difficult problems are being proposed that exceed the capabilities of even the best algorithms currently available. There is, therefore, an immediate need to improve the capabilities of complementarity solvers. This thesis addresses this need in two significant ways. First, the thesis proposes and develops a proximal perturbation strategy that enhances the robustness of Newtonbased complementarity solvers. This strategy enables algorithms to reliably find solutions even for problems whose natural merit functions have strict local minima that are not solutions. Based upon this strategy, three new algorithms are proposed for solving nonlinear mixed complementarity problems that represent a significant improvement in robustness over previous algorithms. These algorithms have local Qquadratic convergence behavior, yet depend only on a pseudomonotonicity assumption to achieve global convergence from arbitrary starting points. Using the MCPLIB and GAMSLIB test libraries, we perform extensive computational tests that demonstrate the effectiveness of these algorithms on realistic problems. Second, the thesis extends some previously existing algorithms to solve more general problem classes. Specifically, the NE/SQP method of Pang & Gabriel (1993), the semismooth equations approach of De Luca, Facchinei & Kanz...
A QMRbased interiorpoint algorithm for solving linear programs
 Math. Programming
, 1997
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Convergence of a class of inexact interiorpoint algorithms for linear programs
 Mathematics of Operations Research
, 1999
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Modified Cholesky Factorizations In InteriorPoint Algorithms For Linear Programming
 SIAM Journal on Optimization
"... . We investigate a modified Cholesky algorithm typical of those used in most interiorpoint codes for linear programming. Choleskybased interiorpoint codes are popular for three reasons: their implementation requires only minimal changes to standard sparse Cholesky algorithms (allowing us to take f ..."
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Cited by 24 (3 self)
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. We investigate a modified Cholesky algorithm typical of those used in most interiorpoint codes for linear programming. Choleskybased interiorpoint codes are popular for three reasons: their implementation requires only minimal changes to standard sparse Cholesky algorithms (allowing us to take full advantage of software written by specialists in that area); they tend to be more efficient than competing approaches that use alternative factorizations; and they perform robustly on most practical problems, yielding good interiorpoint steps even when the coefficient matrix of the main linear system to be solved for the step components is illconditioned. We investigate this surprisingly robust performance by using analytical tools from matrix perturbation theory and error analysis, illustrating our results with computational experiments. Finally, we point out the potential limitations of this approach. Key words. interiorpoint algorithms and software, Cholesky factorization, matrix p...
Solving RealWorld Linear Ordering Problems . . .
, 1995
"... Cutting plane methods require the solution of a sequence of linear programs, where the solution to one provides a warm start to the next. A cutting plane algorithm for solving the linear ordering problem is described. This algorithm uses the primaldual interior point method to solve the linear prog ..."
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Cited by 23 (8 self)
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Cutting plane methods require the solution of a sequence of linear programs, where the solution to one provides a warm start to the next. A cutting plane algorithm for solving the linear ordering problem is described. This algorithm uses the primaldual interior point method to solve the linear programming relaxations. A point which is a good warm start for a simplexbased cutting plane algorithm is generally not a good starting point for an interior point method. Techniques used to improve the warm start include attempting to identify cutting planes early and storing an old feasible point, which is used to help recenter when cutting planes are added. Computational results are described for some realworld problems; the algorithm appears to be competitive with a simplexbased cutting plane algorithm.
Conic convex programming and selfdual embedding
 Optim. Methods and Software
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