### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

APRIL 22, 2016

**Speaker: **
Amitabh Basu, Johns Hopkins University

**Title: ***
Projection: A Unified Approach to Semi-Infinite Linear Optimization and Duality in Convex Programming
*

**Abstract:**
Fourier-Motzkin elimination was invented as an explicit projection algorithm for polyhedra and can be used to encode a lot of information in instances of linear optimization with finitely many constraints.

We extend Fourier-Motzkin elimination to semi-infinite linear programs, i.e., linear optimization problems with finitely many variables and infinitely many constraints. Applying projection leads to new characterizations of important properties for primal-dual pairs of semi-infinite programs such as zero duality gap, feasibility, boundedness, and solvability.

This extension of the Fourier-Motzkin elimination procedure yields a new classification of variables that is used to determine the existence of duality gaps. Our approach has interesting applications in finite-dimensional convex optimization, such as completely new proofs of classical sufficient conditions for zero duality like Slater's condition. Time permitting, I will also mention some new insights obtained from this approach into the the structure of semi-infinite linear programs.

**Time:** Friday, April 22, 2016, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491