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Browsing by Author "Coleman, Thomas F."
Now showing items 1938 of 64

A Global and Quadratic Affine Scaling Method for Linear $L_{1}$ Problems.
Coleman, Thomas F.; Li, Yuying (Cornell University, 198907)Recently, various interior point algorithms  related to the Karmarkar algorithm  have been developed for linear programming. In this paper, we first show how this "interior point" philosophy can be adapted to the ... 
A Global and QuadraticallyConvergent Method for Linear $L_{\infty}$ Problems
Coleman, Thomas F.; Li, Yuying (Cornell University, 199004)We propose a new global and quadratically convergent algorithm for the linear $l_{\infty}$ problem. This method works on the piecewise $l_{\infty}$ problem directly by generating descent directions  via a sequence of ... 
A Globally and Superlinearly Convergent Algorithm for Convex Quadratic Programs with Simple Bounds
Coleman, Thomas F.; Hulbert, Laurie (Cornell University, 199002)We present a globally and superlinearly convergent algorithm for solving convex quadratic programs with simple bounds. We develop our algorithm using a new formulation of the problem: the minimization of an unconstrained ... 
Hedging a Portfolio of derivatives by Modeling Cost
Boyle, Katharyn A.; Coleman, Thomas F.; Li, Yuying (Cornell University, 20030119)We consider the problem of hedging the loss of a given portfolio of derivatives using a set of more liquid derivative instruments. We illustrate why the typical mathematical formulation for this hedging problem is ... 
Hedging a Portfolio of Derivatives by Modeling Cost
Boyle, Katharyn A.; Coleman, Thomas F.; Li, Yuying (Cornell University, 20030122)We consider the problem of hedging the loss of a given portfolio of derivatives using a set of more liquid derivative instruments. We illustrate why the typical mathematical formulation for this hedging problem is illposed. ... 
An Interior Newton Method for Quadratic Programming
Coleman, Thomas F.; Liu, Jianguo (Cornell University, 199310)Quadratic programming represents an extremely important class of optimization problem. In this paper, we propose a new (interior) approach for the general quadratic programming problem. We establish that our new method ... 
An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
Coleman, Thomas F.; Li, Yuying (Cornell University, 199305)We propose a new trust region approach for minimizing a nonlinear function subject to simple bounds. By choosing an appropriate quadratic model and scaling matrix at each iteration, we show that it is not necessary to ... 
Isotropic Effective Energy Simulated Annealing Searches for Low Energy Molecular Cluster States
Coleman, Thomas F.; Shalloway, David; Wu, Zhijun (Cornell University, 199211)The search for low energy states of molecular clusters is associated with the study of molecular conformation and especially protein folding. This paper describes a new global minimization algorithm which is effective ... 
LargeScale Numerical Optimization: Introduction and Overview
Coleman, Thomas F. (Cornell University, 199109)We give an introductory overview of the field of largescale numerical optimization; some of the basic research issues and recent developments are described. Our emphasisis on methods, techniques, and practical concerns. ... 
A New Method for Solving Triangular Systems on Distributed Memory MessagePassing Multiprocessors
Li, Guangye; Coleman, Thomas F. (Cornell University, 198703)Efficient triangular solvers for use on message passing multiprocessors are required, in several contexts, under the assumption that the matrix is distributed by columns (or rows) in a wrap fashion. In this paper we ... 
A New Trust Region Algorithm for Equality Constrained Optimization
Coleman, Thomas F.; Yuan, Wei (Cornell University, 199501)We present a new trust algorithm for solving nonlinear equality constrained optimization problems. At each iterate a change of variables is performed to improve the ability of the algorithm to follow the constraint level ... 
A New Trust Region algorithm for Equality Constrained Optimization
Coleman, Thomas F.; Yuan, Wei (Cornell University, 199503)We present a new trust region algorithms for solving nonlinear equality constrained optimization problems. At each iterate a change of variables is performed to improve the ability of the algorithm to follow the constraint ... 
A Newton Method for American Option Pricing
Coleman, Thomas F.; Li, Yuying; Verma, Arun (Cornell University, 20030123)The variational inequality formulation provides a mechanism to determine both the option value and the early exercise curve implicitly [17]. Standard finite difference approximation typically leads to linear complementarity ... 
A Note on the Computation of an Orthonormal Basis for the Null Space of a Matrix
Coleman, Thomas F.; Sorensen, Danny C. (Cornell University, 198208)A highly regarded method to obtain an orthonormal basis, $Z$, for the null space of a matrix $A^{T}$ is the $QR$ decomposition of $A$, where $Q$ is the product of Householder matrices. In several optimization contexts ... 
The Null Space Problem II: Algorithms
Coleman, Thomas F.; Pothen, Alex (Cornell University, 198604)The Null Space Problem is that of finding a sparsest basis for the null space (null basis) of a $t \times n$ matrix of rank $t$. This problem was shown to be NPhard in Coleman and Pothen (1985). In this paper we develop ... 
On Characterizations of Superlinear Convergence for Constrained Optimization
Coleman, Thomas F. (Cornell University, 198808)We show how the DennisMore characterization of superlinear convergence for unconstrained optimization can be applied, and usefully restricted for use in the constrained setting. 
On The Convergence of Reflective Newton Methods for LargeScale Nonlinear Minimization Subject to Bounds
Coleman, Thomas F.; Li, Yuying (Cornell University, 199211)We consider a new algorithm, a reflective Newton method, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generates ... 
On the Convergence of Reflective Newton Methods for Largescale Nonlinear Minimization Subject to Bounds
Coleman, Thomas F.; Li, Yuying (Cornell University, 199211)We consider a new algorithm, a reflective Newton method, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach ... 
On the Local Convergence of a QuasiNewton Method for the Nonlinear Programming Problem
Coleman, Thomas F.; Conn, Andrew R. (Cornell University, 198208)In this paper we propose a new local quasiNewton method to solve the equality constrained nonlinear programming problem. The pivotal feature of the algorithm is that a projection of the Hessian of the Lagrangian is ... 
On The Local Convergence of The ByrdSchnabel Algorithm For Constrained Optimization
Coleman, Thomas F.; Liao, AiPing (Cornell University, 199202)Most reduced Hessian methods for equality constrained problems use a basis for the null space of the matrix of constraint gradients and posess superlinearly convergent rates under the assumption of continuity of the ...