Symbolic computation of multidimensional Fenchel conjugates

Authors:
Jonathan M. Borwein;Chris H. Hamilton
Affiliations:
Dalhousie University, Halifax, NS, Canada;Dalhousie University, Halifax, NS, Canada
Venue:
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Year:
2006

Citing 5
Cited 1

Fast Legendre--Fenchel Transform and Applications to Hamilton--Jacobi Equations and Conservation Laws

SIAM Journal on Numerical Analysis
A fast computational algorithm for the Legendre-Fenchel transform

Computational Optimization and Applications
Optimization by Vector Space Methods

Optimization by Vector Space Methods
Convex Optimization

Convex Optimization
A procedure for proving special function inequalities involving a discrete parameter

Proceedings of the 2005 international symposium on Symbolic and algebraic computation

A canonical form for piecewise defined functions

Proceedings of the 2007 international symposium on Symbolic and algebraic computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Convex optimization is a branch of mathematics dealing with non-linear optimization problems with additional geometric structure. This area has been the focus of considerable recent research due to the fact that convex optimization problems are scalable and can be efficiently solved by interior-point methods. Over the last ten years or so, convex optimization has found new applications in many areas including control theory, signal processing, communications and networks, circuit design, data analysis and finance.Of key importance in convex optimization is the notion of duality, and in particular that of Fenchel duality. This work explores algorithms for calculating symbolic Fenchel conjugates of a class of real-valued functions defined on Rn, extending earlier work to the non-separable multi-dimensional case. It also explores the potential application of the developed algorithms to automatic inequality proving.