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Browsing by Author "Coleman, Thomas F."
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Advanced Computing Research Institute Semiannual Research Activity Report, April 1992  September 1992
Coleman, Thomas F. (Cornell University, 199211)The Advanced Computing Research Institute (ACRI) is a unit of the Cornell Theory Center and is affiliated with the Cornell Computer Science Department. The ACRI is concerned with research in scientific computation ... 
A Chordal Preconditioner for Large Scale Optimization
Coleman, Thomas F. (Cornell University, 198606)We propose an automatic preconditioning scheme for large sparse numerical optimization. The strategy is based on an examination of the sparsity pattern of the Hessian matrix: using a graphtheoretic heuristic, a block ... 
Computing a Trust Region Step for a Penalty Function
Coleman, Thomas F.; Hempel, Christian (Cornell University, 198707)We consider the problem of minimizing a quadratic function subject to an ellipsoidal constraint when the matrix involved is the Hessian of a quadratic penalty function (i.e., a function of the form $p(x) = f(x) + ... 
The Cyclic Coloring Problem and Estimation of Sparse Hessian Matrices
Coleman, Thomas F.; Cai, Jinyi (Cornell University, 198410)Numerical optimization algorithms often require the (symmetric) matrix of second derivatives, $\nabla^{2} f (x)$, of some problem function $f: R^{n} \rightarrow R^{1}$. If the Hessian matrix is large and sparse then ... 
A Direct Active Set Algorithm for Large Sparse Quadratic Programs withSimple Bounds
Coleman, Thomas F.; Hulbert, Laurie (Cornell University, 198807)We show how a direct active set method for solving definite and indefinite quadratic programs with simple bounds can be efficiently implemented for large sparse problems. All of the necessary factorizations can be carried ... 
Discrete Hedging Under Piecewise Linear Risk Management
Coleman, Thomas F.; Li, Yuying; Patron, MariaCristina (Cornell University, 20030122)In an incomplete market it is usually impossible to eliminate the intrinsic risk of an option. In this case quadratic riskminimization is often used to determine a hedging strategy. However, it may be more natural to use ... 
Dynamic Hedging in a Volatile Market
Coleman, Thomas F.; Kim, Yohan; Li, Yuying; Verma, Arun (Cornell University, 20030123)In financial markets, errors in option hedging can arise from two sources. First, the option value is a nonlinear function of the underlying; therefore, hedging is instantaneous and hedging with discrete rebalancing gives ... 
Dynamic Hedging With a Deterministic Local Volatility Function Model
Coleman, Thomas F.; Kim, Y.; Li, Y.; Verma, A. (Cornell University, 20030123)We compare the dynamic hedging performance of the deterministic local volatility function approach with the implied/constant volatility method. Using an example in which the underlying price follows an absolute diffusion ... 
Dynamic Hedging with a Deterministic Local Volatility Function Model
Coleman, Thomas F.; Kim, Yohan; Li, Yuying; Verma, Arun (Cornell University, 20030123)We compare the dynamic hedging performance of the deterministic local volatility function approach with the implied/constant volatility method. Using an example in which the underlying price follows an absolute diffusion ... 
Efficient Calculation of Jacobian and Adjoint Vector Products in Wave Propagational Inverse Problems Using Automatic Differentiation
Coleman, Thomas F.; Santosa, Fadil; Verma, Arun (Cornell University, 20030123)Wave propagational inverse problems arise in several applications including medical imaging and geophysical exploration. In these problems, one is interested in obtaining the parameters describing the medium from its ... 
Efficient Calculation of Jacobian and Adjoint Vector Products in Wave Propagational Inverse Problems Using Automatic Differentiation
Coleman, Thomas F.; Santosa, Fadil; Verma, Arun (Cornell University, 20030122)Wave propagational inverse problems arise in several applications including medical imaging and geophysical exploration. In these problems, one is interested in obtaining the parameters describing the medium from its ... 
The Efficient Computation of Sparse Jacobian Matrices Using Automatic Differentiation
Coleman, Thomas F.; Verma, Arun (Cornell University, 199512)This paper is concerned with the efficient computation of sparse Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of a graph coloring technique, bicoloring, ... 
The efficient computation of sparse Jacobian matrices using automaticdifferentiation
Coleman, Thomas F.; Verma, Arun (Cornell University, 199511)This paper is concerned with the efficient computation of sparse Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of a graph coloring technique, bicoloring, ... 
An efficient trust region method for unconstrained discretetime optimal control problems
Coleman, Thomas F.; Liao, Aiping (Cornell University, 20031111)Discretetime optimal control (DTOC) problems are largescale optimization problems with a dynamic structure. In previous work this structure has been exploited to provide very fast and efficient local procedures. Two ... 
An Efficient Trust Region Method for Unconstrained DiscreteTime Optimal Control Problems
Coleman, Thomas F.; Liao, Aiping (Cornell University, 199307)Discretetime optimal control (DTOC) problems are largescaleoptimization problems with a dynamic structure. In previous work this structure has been exploited to provide very fast and efficient local procedures. Two ... 
Estimation of Sparse Hessian Matrices and Graph Coloring Problems
Coleman, Thomas F.; More, Jorge J. (Cornell University, 198212)Large scale optimization problems often require an approximation to the Hessian matrix. If the Hessian matrix is sparse then estimation by differences of gradients is attractive because the number of required differences ... 
An Exterior Newton Method for Convex Quadratic Programming
Coleman, Thomas F.; Liu, Jianguo (Cornell University, 199710)We propose an exterior Newton method for convex quadratic programming problems. 
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 ...