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An Algorithm for Nonlinear Optimization Using Linear Programming and Equality Constrained Subproblems
, 2003
"... This paper describes an activeset algorithm for largescale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the activ ..."
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Cited by 38 (12 self)
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This paper describes an activeset algorithm for largescale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the ` 1 penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active at the solution of the linear program.
An Algorithm for the Fast Solution of Symmetric Linear Complementarity Problems
, 2008
"... This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improveme ..."
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Cited by 6 (1 self)
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This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American options pricing. The paper proposes an improvement of a method described by Kocvara and Zowe [19] that combines projected GaussSeidel iterations with subspace minimization steps. The proposed algorithm employs a recursive subspace minimization designed to handle severely illconditioned problems. Numerical tests indicate that the approach is more efficient than interiorpoint and gradient projection methods on some physical simulation problems that arise in computer game scenarios.
An activeset algorithm for nonlinear programming using linear programming and equality constrained subproblems
, 2002
"... This paper describes an activeset algorithm for largescale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [9]. The step computation is performed in two stages. In the rst stage a linear program is solved to estimate the active set ..."
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Cited by 6 (1 self)
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This paper describes an activeset algorithm for largescale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [9]. The step computation is performed in two stages. In the rst stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the `1 penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active atthesolution of the linear program. The EQP incorporates a trustregion constraint and is solved (inexactly) by means of a projected conjugate gradient method. Numerical experiments are presented illustrating the performance of the algorithm on the CUTEr [1] test set.
A Numerical Study of ActiveSet and InteriorPoint Methods for Bound Constrained Optimization ⋆
"... Summary. This papers studies the performance of several interiorpoint and activeset methods on bound constrained optimization problems. The numerical tests show that the sequential linearquadratic programming (SLQP) method is robust, but is not as effective as gradient projection at identifying th ..."
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Summary. This papers studies the performance of several interiorpoint and activeset methods on bound constrained optimization problems. The numerical tests show that the sequential linearquadratic programming (SLQP) method is robust, but is not as effective as gradient projection at identifying the optimal active set. Interiorpoint methods are robust and require a small number of iterations and function evaluations to converge. An analysis of computing times reveals that it is essential to develop improved preconditioners for the conjugate gradient iterations used in SLQP and interiorpoint methods. The paper discusses how to efficiently implement incomplete Cholesky preconditioners and how to eliminate illconditioning caused by the barrier approach. The paper concludes with an evaluation of methods that use quasiNewton approximations to the Hessian of the Lagrangian. 1
An Algorithm for Nonlinear Optimization Using Linear Programming and Equality Constrained Subproblems
, 2003
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Learning with DegreeBased Subgraph Estimation
, 2011
"... Networks and their topologies are critical to nearly every aspect of modern life, with social networks governing human interactions and computer networks governing global informationflow. Network behavior is inherently structural, and thus modeling data from networks benefits from explicitly modeli ..."
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Networks and their topologies are critical to nearly every aspect of modern life, with social networks governing human interactions and computer networks governing global informationflow. Network behavior is inherently structural, and thus modeling data from networks benefits from explicitly modeling structure. This thesis covers methods for and analysis of machine learning from network data while explicitly modeling one important measure of structure: degree. Central to this work is a procedure for exact maximum likelihood estimation of a distribution over graph structure, where the distribution factorizes into edgelikelihoods for each pair of nodes and degreelikelihoods for each node. This thesis provides a novel method for exact estimation of the maximum likelihood edge structure under the distribution. The algorithm solves the optimization by constructing an augmented graph containing, in addition to the original nodes, auxiliary nodes whose edges encode the degree potentials. The exact solution is then recoverable by finding the maximum weight bmatching on the augmented graph, a wellstudied combinatorial optimization. To solve the combinatorial optimization, this thesis focuses in particular on a belief propagationbased approach to finding the optimal bmatching and provides a novel proof of convergence for belief propagation on the loopy graphical model representing the bmatching objective. Additionally,