numerical algorithm – Optimization Online

Fast Moreau Envelope Computation I: Numerical Algorithms

Published: 2005/10/05, Updated: 2007/01/08

Convex Optimization, Nonsmooth Optimization, Problem Solving Environments conjugate, discrete legendre transform, envelope of functions, legendre-fenchel transform, linear-time worst-case complexity, moreau-yosida approximate, numerical algorithm

The present article summarizes the state of the art algorithms to compute the discrete Moreau envelope, and presents a new linear-time algorithm, named NEP for NonExpansive Proximal mapping. Numerical comparisons between the NEP and two existing algorithms: The Linear-time Legendre Transform (LLT) and the Parabolic Envelope (PE) algorithms are performed. Worst-case time complexity, convergence results, … Read more

NLPQLP: A New Fortran Implementation of a Sequential Quadratic Programming Algorithm

Published: 2002/01/10

Klaus Schittkowski

Constrained Nonlinear Optimization, Optimization Software Benchmark, Parallel Algorithms distributed computing, fortran code, line-search, nonlinear programming, numerical algorithm, performance evaluation, sequential quadratic programming

The Fortran subroutine NLPQLP solves smooth nonlinear programming problems and is an extension of the code NLPQL. The new version is specifically tuned to run under distributed systems. A new input parameter l is introduced for the number of parallel machines, that is the number of function calls to be executed simultaneously. In case of … Read more