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Browsing by Author "More, Jorge J."
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The Application of Variational Inequalities to Complementarity Problems and Existence Theorems
More, Jorge J. (Cornell University, 197110)If $F : C \rightarrow R^{n}$ is a continuous (nonlinear) mapping on a closed, convex subset $C$ of $R^{n}$, it is shown that very weak coercivity conditins on $F$ guarantee the existence of a solution $x^{*} in $C$ to the ... 
A Characterization of Superlinear Convergence and its Application to QuasiNewton Methods
Dennis, John E., Jr.; More, Jorge J. (Cornell University, 197301)Let F be a mapping from real ndimensional Euclidean space into itself. Most practical algorithms for finding a zero of F are of the form $x_{k+1} = x_{k}  B_{k}^{1_{Fx_{k}}}$ where $\{B_{k}\}$ is a sequence of nonsingular ... 
A Characterization of Superlinear Convergence and its Application to QuasiNewton Methods
Dennis, John E., Jr.; More, Jorge J. (Cornell University, 197301)Let F be a mapping from real ndimensional Euclidean space into itself. Most practical algorithms for finding a zero of F are of the form $x_{k+1} = x_{k}  B_{k}^{1_{Fx_{k}}}$ where $\{B_{k}\}$ is a sequence of nonsingular ... 
Classes of Functions and Feasibility Conditions in Nonlinear Complimentarity Problems
More, Jorge J. (Cornell University, 197306)Given a mapping $F$ from real Euclidean nspace into itself, we investigate the connection between various known classes of functions and the nonlinear complementarity problem: Find and $x^{*} \geq 0$ such that $ F x^{*} ... 
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 ... 
Nonlinear Generalizations of Matrix Diagonal Dominance with Application to GaussSeidel Iterations
More, Jorge J. (Cornell University, 197101)A new class of nonlinear mappings is introduced which contains, in the linear case, the strictly and irreducibly diagonally dominant matrices as well as other classes of matrices introduced by Duffin and Walter. We then ... 
On the Global Convergence of Broyden's Method
More, Jorge J.; Trangenstein, J. A. (Cornell University, 197410)We consider Broyden's 1965 method for solving nonlinear equations. If the mapping is linear, then a simple modification of this method guarantees global and Qsuperlinear convergence. For nonlinear mappings it is shown ... 
QuasiNewton Methods, Motivation and Theory
Dennis, John E., Jr.; More, Jorge J. (Cornell University, 197411)This paper is an attempt to motivate and justify quasiNewton methods as useful modifications of Newton's method for general and gradient nonlinear systems of equations. References are given to ample numerical justification; ... 
Software For Estimating Sparse Hessian Matrices
Coleman, Thomas F.; Garbow, Burton S.; More, Jorge J. (Cornell University, 198501)The solution of a nonlinear optimization problem often requires an estimate of the Hessian matrix for a function $f$. In large scale problems the Hessian matrix is usually sparse, and then estimation by differences of ... 
Software for Estimating Sparse Jacobian Matrices
Coleman, Thomas F.; More, Jorge J. (Cornell University, 198206)In many nonlinear problems it is necessary to estimate the Jacobian matrix of a nonlinear mapping $F$. In large scale problems the Jacobian of $F$ is usually sparse, and then estimation by differences is attractive because ...