Results 1 
6 of
6
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 ..."
Abstract

Cited by 39 (12 self)
 Add to MetaCart
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 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 ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
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.
On the Use of Piecewise Linear Models in Nonlinear Programming
, 2010
"... This paper presents an activeset algorithm for largescale optimization that occupies the middle ground between sequential quadratic programming (SQP) and sequential linearquadratic programming (SLQP) methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximati ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
This paper presents an activeset algorithm for largescale optimization that occupies the middle ground between sequential quadratic programming (SQP) and sequential linearquadratic programming (SLQP) methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the constraints, to determine a working set. Then, an equality constrained subproblem based on this working set and using second derivative information is solved in order to promote fast convergence. A study of the local and global convergence properties of the algorithm highlights the importance of the placement of the interpolation points that determine the piecewise linear model of the Lagrangian. 1
An Algorithm for Nonlinear Optimization Using Linear Programming and Equality Constrained Subproblems
, 2003
"... 1 ..."
RESEARCH ARTICLE Mixed Integer Nonlinear Programming Using InteriorPoint Methods
"... In this paper, we outline a bilevel approach for solving mixed integer nonlinear programming problems. The approach combines a branchandbound algorithm in the outer iterations and an infeasible interiorpoint method in the inner iterations. We report on the details of the implementation, including ..."
Abstract
 Add to MetaCart
In this paper, we outline a bilevel approach for solving mixed integer nonlinear programming problems. The approach combines a branchandbound algorithm in the outer iterations and an infeasible interiorpoint method in the inner iterations. We report on the details of the implementation, including the efficient pruning of the branchandbound tree via equilibrium constraints, warmstart strategies for interiorpoint methods, and the handling of infeasible subproblems, and present numerical results on a standard problem library. Our goal is to demonstrate the viability of interiorpoint methods, with suitable modifications, to be used within any MINLP framework, and the numerical results provided are quite encouraging.
On the Convergence of Successive LinearQuadratic Programming Algorithms
, 2005
"... Abstract The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches, and more specifically, the successive linearquadratic programming approachpresented by Byrd, Gould, Nocedal and Waltz (Ma ..."
Abstract
 Add to MetaCart
Abstract The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches, and more specifically, the successive linearquadratic programming approachpresented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):2748, 2004). Every iteration requires the solution of two trustregion subproblems involvingpiecewise linear and quadratic models, respectively. It is shown that, for a fixed penalty parameter, the sequence of iterates approaches stationarity of the penalty function. Aprocedure for dynamically adjusting the penalty parameter is described, and global convergence results for it are established.