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Extending the Farkas Lemma Approach to Necessity Conditions to Infinite Programming
Under mild assumptions, the classical Farkas lemma approach to Lagrange multiplier theory is extended to an infinite programming formulation. The main result generalizes the usual first-order necessity conditions to address ...
Analysis of Explicit/Implicit, Block Centered Finite Difference Domain Decomposition Procedures for Parabolic Problems
Domain decomposition procedures for solving parabolic equations are considered. The underlying discretization is block-centered finite differences. In this procedures, fluxes at subdomain interfaces are calculated from the ...
An Implementation of a Parallel Primal-Dual Interior Point Method for Multicommodity Flow Problems
An implementation of the primal-dual predictor-corrector interior point method is specialized to solve linear multicommodity flow problems. The block structure of the constraint matrix is exploited via parallel computation. ...
Successive Element Correction Algorithms for Sparse Unconstrained Optimization
This paper presents a successive element correction algorithm and a secant modification of this algorithm. The new algorithms are designed to use the gradient evaluations as efficiently as possible in forming the approximate ...
Steady State Couette Flow
An exact solution is found for a non-linear problem with thermomechanical coupling, the steady flow of a fluid with viscosity exponentially dependent on temperature, which is sheared between an adiabatic, fixed, inner ...
Column-Secant Update Technique for Solving Systems of Nonlinear Equations
This paper presents a QR update implementation of the successive column correction (SCC) method and a column-secant modification of the SCC method, which is called the CSSCC method. The computational cost of the QR update ...
A Diagonal-Secant Update Technique for Sparse Unconstrained Optimization
This paper presents a diagonal-secant modification of the successive element correction method, a finite-difference based method, for sparse unconstrained optimization. This new method uses the gradient values more efficiently ...
Conventions for Using PIERS