Results 1  10
of
22
Newton's Method For Large BoundConstrained Optimization Problems
 SIAM JOURNAL ON OPTIMIZATION
, 1998
"... We analyze a trust region version of Newton's method for boundconstrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearlyconstrained problems, and yields global and super ..."
Abstract

Cited by 108 (5 self)
 Add to MetaCart
We analyze a trust region version of Newton's method for boundconstrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearlyconstrained problems, and yields global and superlinear convergence without assuming neither strict complementarity nor linear independence of the active constraints. We also show that the convergence theory leads to an efficient implementation for large boundconstrained problems.
A Globally Convergent PrimalDual InteriorPoint Filter Method for Nonlinear Programming
, 2002
"... In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interiorpoint algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primaldual step obtained from the p ..."
Abstract

Cited by 52 (4 self)
 Add to MetaCart
In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interiorpoint algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primaldual step obtained from the perturbed firstorder necessary conditions into a normal and a tangential step, whose sizes are controlled by a trustregion type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to firstorder critical points is proved for the new primaldual interiorpoint filter algorithm.
A new active set algorithm for box constrained optimization,”
 SIAM Journal on Optimization,
, 2006
"... ..."
NonMonotone TrustRegion Methods for BoundConstrained Semismooth Equations with Applications to Nonlinear Mixed Complementarity Problems
, 1999
"... We develop and analyze a class of trustregion methods for boundconstrained semismooth systems of equations. The algorithm is based on a simply constrained differentiable minimization reformulation. Our global convergence results are developed in a very general setting that allows for nonmonotoni ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
We develop and analyze a class of trustregion methods for boundconstrained semismooth systems of equations. The algorithm is based on a simply constrained differentiable minimization reformulation. Our global convergence results are developed in a very general setting that allows for nonmonotonicity of the function values at subsequent iterates. We propose a way of computing trial steps by a semismooth Newtonlike method that is augmented by a projection onto the feasible set. Under a DennisMoretype condition we prove that close to a BDregular solution the trustregion algorithm turns into this projected Newton method, which is shown to converge locally qsuperlinearly or quadratically, respectively, depending on the quality of the approximate BDsubdifferentials used. As an important application we discuss in detail how the developed algorithm can be used to solve nonlinear mixed complementarity problems (MCPs). Hereby, the MCP is converted into a boundconstrained semismooth...
An interior point Newtonlike method for nonnegative least squares problems with degenerate solution
 Numer. Linear Algebra Appl
"... Abstract. An interior point approach for medium and large nonnegative linear leastsquares problems is proposed. Global and locally quadratic convergence is shown even if a degenerate solution is approached. Viable approaches for implementation are discussed and numerical results are provided. ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
(Show Context)
Abstract. An interior point approach for medium and large nonnegative linear leastsquares problems is proposed. Global and locally quadratic convergence is shown even if a degenerate solution is approached. Viable approaches for implementation are discussed and numerical results are provided.
On affinescaling interiorpoint Newton methods for nonlinear minimization with bound constraints
 Computational Optimization and Applications
"... Abstract. A class of new affinescaling interiorpoint Newtontype methods are considered for the solution of optimization problems with bound constraints. The methods are shown to be locally quadratically convergent under the strong second order sufficiency condition without assuming strict compl ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
(Show Context)
Abstract. A class of new affinescaling interiorpoint Newtontype methods are considered for the solution of optimization problems with bound constraints. The methods are shown to be locally quadratically convergent under the strong second order sufficiency condition without assuming strict complementarity of the solution. The new methods differ from previous ones by Coleman and Li [Mathematical Programming, 67 (1994), pp. 189– 224] and Heinkenschloss, Ulbrich, and Ulbrich [Mathematical Programming, 86 (1999), pp. 615–635] mainly in the choice of the scaling matrix. The scaling matrices used here have stronger smoothness properties and allow the application of standard results from nonsmooth analysis in order to obtain a relatively short and elegant local convergence result. An important tool for the definition of the new scaling matrices is the correct identification of the degenerate indices. Some illustrative numerical results with a comparison of the different scaling techniques are also included. Key Words. Newton’s method, affine scaling, interiorpoint method, quadratic convergence, identification of active constraints. 1
A Reduced Newton Method for Constrained Linear LeastSquares Problems
"... We propose an iterative method that solves constrained linear leastsquares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown varia ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
(Show Context)
We propose an iterative method that solves constrained linear leastsquares problems by formulating them as nonlinear systems of equations and applying the Newton scheme. The method reduces the size of the linear system to be solved at each iteration by considering only a subset of the unknown variables. Hence the linear system can be solved more efficiently. We prove that the method is locally quadratic convergent. Applications to image deblurring problems show that our method gives better restored images than those obtained by projecting or scaling the solution into the dynamic range.
InteriorPoint Gradient Methods with DiagonalScalings for SimpleBound Constrained Optimization
, 2004
"... In this paper, we study diagonally scaled gradient methods for simplebound constrained optimization in a framework almost identical to that for unconstrained optimization, except that iterates are kept within the interior of the feasible region. We establish a satisfactory global convergence the ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
In this paper, we study diagonally scaled gradient methods for simplebound constrained optimization in a framework almost identical to that for unconstrained optimization, except that iterates are kept within the interior of the feasible region. We establish a satisfactory global convergence theory for such interiorpoint gradient methods applied to Lipschitz continuously di#erentiable functions without any further assumption. Moreover,
A local convergence property of primaldual methods for nonlinear programming
 MATH. PROGRAM., SER. A
, 2006
"... ..."