Results 1 
8 of
8
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 ..."
Abstract

Cited by 121 (3 self)
 Add to MetaCart
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 Global Convergence Theory for General TrustRegionBased Algorithms for Equality Constrained Optimization
 SIAM Journal on Optimization
, 1992
"... This work presents a global convergence theory for a broad class of trustregion algorithms for the smooth nonlinear progro.mmln S problem with equality constraints. The main result generalizes Powell's 1975 result for unconstrained trustregion algorithms. ..."
Abstract

Cited by 47 (10 self)
 Add to MetaCart
(Show Context)
This work presents a global convergence theory for a broad class of trustregion algorithms for the smooth nonlinear progro.mmln S problem with equality constraints. The main result generalizes Powell's 1975 result for unconstrained trustregion algorithms.
Reduced SQP Methods for LargeScale Optimal Control Problems in DAE with Application to Path Planning Problems for Satellite Mounted Robots
, 1996
"... and loving encouragement. Contents 1 Introduction 3 1.1 The mathematical problem formulation : : : : : : : : : : : : : : : : : : : : 7 1.2 Notational conventions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2 The Collocation Discretization 11 2.1 Collocation for two point BVP in ..."
Abstract

Cited by 19 (7 self)
 Add to MetaCart
and loving encouragement. Contents 1 Introduction 3 1.1 The mathematical problem formulation : : : : : : : : : : : : : : : : : : : : 7 1.2 Notational conventions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2 The Collocation Discretization 11 2.1 Collocation for two point BVP in ODE : : : : : : : : : : : : : : : : : : : : 11 2.1.1 Choice of collocation points : : : : : : : : : : : : : : : : : : : : : : 14 2.1.2 The polynomial representation : : : : : : : : : : : : : : : : : : : : : 14 2.1.3 A tempting combination : : : : : : : : : : : : : : : : : : : : : : : : 15 2.2 Collocation for BVP in DAE with invariants : : : : : : : : : : : : : : : : : 17 2.2.1 DAE models from mechanics : : : : : : : : : : : : : : : : : : : : : : 17 2.2.2 Collocation discretization of two point BVP in DAE : : : : : : :
On the realization of the Wolfe conditions in reduced quasiNewton methods for equality constrained optimization
 SIAM Journal on Optimization
, 1997
"... Abstract. This paper describes a reduced quasiNewton method for solving equality constrained optimization problems. A major difficulty encountered by this type of algorithm is the design of a consistent technique for maintaining the positive definiteness of the matrices approximating the reduced He ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Abstract. This paper describes a reduced quasiNewton method for solving equality constrained optimization problems. A major difficulty encountered by this type of algorithm is the design of a consistent technique for maintaining the positive definiteness of the matrices approximating the reduced Hessian of the Lagrangian. A new approach is proposed in this paper. The idea is to search for the next iterate along a piecewise linear path. The path is designed so that some generalized Wolfe conditions can be satisfied. These conditions allow the algorithm to sustain the positive definiteness of the matrices from iteration to iteration by a mechanism that has turned out to be efficient in unconstrained optimization.
A Merit Function for Inequality Constrained Nonlinear Programming Problems
 Internal Report 4702, National Institute of Standards and Technology
, 1993
"... We consider the use of the sequential quadratic programming (SQP) technique for solving the inequality constrained minimization problem min x f(x) subject to: g i (x) 0; i = 1; : : : ; m: SQP methods require the use of an auxiliary function, called a merit function or linesearch function, for asse ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
We consider the use of the sequential quadratic programming (SQP) technique for solving the inequality constrained minimization problem min x f(x) subject to: g i (x) 0; i = 1; : : : ; m: SQP methods require the use of an auxiliary function, called a merit function or linesearch function, for assessing the steps that are generated. We derive a merit function by adding slack variables to create an equality constrained problem and then using the merit function developed earlier by the authors for the equality constrained case. We stress that we do not solve the slack variable problem, but only use it to construct the merit function. The resulting function is simplified in a certain way that leads to an effective procedure for updating the squares of the slack variables. A globally convergent algorithm, based on this merit function, is suggested, and is demonstrated to be effective in practice. Contribution of the National Institute of Standards and Technology and not subject to copyr...
A Piecewise LineSearch Technique for Maintaining the Positive Definiteness of the Matrices in the SQP Method
, 1997
"... Abstract. A technique for maintaining the positive definiteness of the matrices in the quasiNewton version of the SQP algorithm is proposed. In our algorithm, matrices approximating the Hessian of the augmented Lagrangian are updated. The positive definiteness of these matrices in the space tangent ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. A technique for maintaining the positive definiteness of the matrices in the quasiNewton version of the SQP algorithm is proposed. In our algorithm, matrices approximating the Hessian of the augmented Lagrangian are updated. The positive definiteness of these matrices in the space tangent to the constraint manifold is ensured by a socalled piecewise linesearch technique, while their positive definiteness in a complementary subspace is obtained by setting the augmentation parameter. In our experiment, the combination of these two ideas leads to a new algorithm that turns out to be more robust and often improves the results obtained with other approaches.
A Subgradient Algorithm for Nonlinear Integer Programming
, 1991
"... . This paper describes a subgradient approach to nonlinear integer programming and, in particular, nonlinear 01 integer programming. In this approach, the objective function for a nonlinear integer program is considered as a nonsmooth function over the integer points. The subgradient and the suppor ..."
Abstract
 Add to MetaCart
(Show Context)
. This paper describes a subgradient approach to nonlinear integer programming and, in particular, nonlinear 01 integer programming. In this approach, the objective function for a nonlinear integer program is considered as a nonsmooth function over the integer points. The subgradient and the supporting plane for the function are defined, and a necessary and sufficient condition for the optimal solution is established, based on the theory of nonsmooth analysis. A new algorithm, called the subgradient algorithm, is developed. The algorithm is in some sense an extension of Newton's method to discrete problems: The algorithm searches for a solution iteratively among the integer points. In each iteration, it generates the next point by solving the problem for a local piecewise linear model. Each local model is constructed using the supporting planes for the objective function at a set of previously generated integer points. A solution is found when either the optimality condition is satisf...
ANZIAM J. 45(2003), 91–114 NUMERICAL ALGORITHMS FOR CONSTRAINED MAXIMUM LIKELIHOOD ESTIMATION
, 2002
"... This paper describes a SQPtype algorithm for solving a constrained maximum likelihood estimation problem that incorporates a number of novel features. We call it MLESOL. MLESOL maintains the use of an estimate of the Fisher information matrix to the Hessian of the negative loglikelihood but also e ..."
Abstract
 Add to MetaCart
(Show Context)
This paper describes a SQPtype algorithm for solving a constrained maximum likelihood estimation problem that incorporates a number of novel features. We call it MLESOL. MLESOL maintains the use of an estimate of the Fisher information matrix to the Hessian of the negative loglikelihood but also encompasses a secant approximation S to the secondorder part of the augmented Lagrangian function along with tests for when to use this information. The local quadratic model used has a form something like that of Tapia’s SQP augmented scale BFGS secant method but explores the additional structure of the objective function. The step choice algorithm is based on minimising a local quadratic model subject to the linearised constraints and an elliptical trust region centred at the current approximate minimiser. This is accomplished using the Byrd and Omojokun trust region approach, together with a special module for assessing the quality of the step thus computed. The numerical performance of MLESOL is studied by means of an example involving the estimation of a mixture density. 1.