Browsing Computational and Applied Mathematics by Title
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A Generalized Trust Region Algorithm for Equality Constrained Optimization
(200312)We introduce and analyze a class of generalized trust region sequential quadratic programming (GTRSQP) algorithms for equality constrained optimization. Unlike in standard trust region SQP (TRSQP) algorithms, the optimization ... 
A Geometric Approach to Fluence Map Optimization in IMRT Cancer Treatment Planning
(200407)Intensitymodulated radiation therapy (IMRT) is a stateoftheart technique for administering radiation to cancer patients. The goal of a treatment is to deliver a prescribed amount of radiation to the tumor, while limiting ... 
A Geometric BuildUp Algorithm for Soving the Molecular Distance Geometry Problem with Sparse Distance Data
(200108)Nuclear magnetic resonance (NMR) structure modeling usually produces a sparse set of interatomic distances in protein. In order to calculate the threedimensional structure of protein, current approaches need to estimate ... 
A Global Convergence Theory for a Class of Trust Region Algorithms for Constrained Optimization
(198805)In this research we present a trust region algorithm for solving the equality constrained optimization problem. This algorithm is a variant of the 1984 CelisDennisTapia algorithm. The augmented Lagrangian function is ... 
A Global Convergence Theory for a TrustRegion Algorithm for Constrained Optimization Which Does Not Assume Linear Independence
(199311)A trustregion algorithm for solving the equality constrained optimization problem is presented. This algorithm uses Byrd and Omojokun's way of computing the trial steps, but it differs from the Byrd and Omojokun algorithm ... 
A Global Convergence Theory for Arbitrary Norm Trust Region Methods for Nonlinear Equations
(198703)In this research we extend the LevenbergMarquardt algorithm for approximating zeros of the nonlinear system F(x) = 0, where F is continuously differentiable from R^n to R^n. Instead of the l2norm, arbitrary norms can ... 
A Global Convergence Theory for Arbitrary Norm TrustRegion Algorithms for Equality Constrained Optimization
(199312)In this paper, we propose a trustregion algorithm to minimize a nonlinear function f: R^n > R subject to nonlinear equality constraints hi (x)=0, i=1, ..., m where hi: R^n > R. We are concerned with the fact that n and m may ... 
A Global Convergence Theory for Arbitrary Norm TrustRegion Methods for Nonlinear Equations
(199309)In this work we extend the LevenbergMarquardt algorithm for approximating zeros of the nonlinear system F(x) = 0, where F : R^n > R^n is continuously differentiable. Instead of the l2 norm, arbitrary norms can be used ... 
A Global Convergence Theory for General TrustRegionBased Algorithms for Equality Constrained Optimization
(199209)This work presents a global convergence theory for a broad class of trustregion algorithms for the smooth nonlinear programming problem with equality constraints. The main result generalizes Powell's 1975 result for ... 
A Global Convergence Theory for the CelisDennisTapia Trust Region Algorithm for Constrained Optimization
(198809)A global convergence theory for a class of trust region algorithms for solving the equality constrained optimization problem is presented. This theory is sufficiently general that it holds for any algorithm that generates ... 
A Global Optimization Method for the Molecular Replacement Problem in Xray Crystallography
(200206)The primary technique for determining the threedimensional structure of a protein molecule is Xray crystallography, from which the molecular replacement (MR) problem often arises as a critical step. The MR problem is a ... 
A Globally Convergent PrimalDual InteriorPoint Filter Method for Nonconvex Nonlinear Programming
(200004)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 ... 
A Home Health Care Routing and Scheduling Problem
(199806)Consider the problem of routing a set of nurses from each individual nurse's home to a set of patients and back home again. Each patient must be visited by a single "feasible" nurse during its time window. Essentially, ... 
A LargeScale TrustRegion Approach to the Regularization of Discrete IllPosed Problems
(199805)We consider the problem of computing the solution of largescale discrete illposed problems when there is noise in the data. These problems arise in important areas such as seismic inversion, medical imaging and signal ... 
A LinearTime Algorithm for Solving the Molecular Distance Geometry Problem with Exact InterAtomic Distances
(200106)We describe a lineartime algorithm for solving the molecular distance geometry problem with exact distances between all pairs of atoms. This problem needs to be solved in every iteration of general distance geometry ... 
A Linearized Bregman Algorithm for Decentralized Basis Pursuit
(201304)We solve a decentralized basis pursuit problem in a multiagent system, where each agent holds part of the linear observations on a common sparse vector, and all the agents collaborate to recover the sparse vector through ... 
A Lumped Finite Element Method for Cap Rock Heat Loss Calculations
(198310)Numerical models of thermal recovery processes arising in petroleum engineering require accurate estimates of the interaction between a reservoir and the surrounding cap and base rock. It is important to obtain an accurate ... 
A MADS Algorithm with a Progressive Barrier for DerivativeFree Nonlinear Programming
(200712)We propose a new algorithm for general constrained derivativefree optimization. As in most methods, constraint violations are aggregated into a single constraint violation function. As in filter methods, a threshold, or ... 
A Matlab Implementation of a Flat Norm Motivated Polygonal Edge Matching Method using a Decomposition of Boundary into Four 1Dimensional Currents
(200909)We describe and provide code and examples for a polygonal edge matching method.