University of Colorado Denver University of Colorado Denver College of Liberal Arts and Sciences
Alexander Engau

Http: Faculty & Staff Directory

Email: Alexander [dot] Engau
[at] UCDenver [dot] edu

Phone: [+1] (303) 315-1719
Fax: [+1] (303) 315-1704

Office: SCB 4223
1201 Larimer Street
Denver, Colorado 80204

Mail: UCD Math & Stats
C Box 170, PO Box 173364
Denver, CO 80217-3364

Alexander Engau

(You may download my card for contact information only.)

Alexander Engau, Assistant Professor

Math 7593 Advanced Linear Programming

Below, please find the most recent description of this course as taught during the Spring of 2010. An updated syllabus, class materials and lectures notes will be posted before the course is offered the next time, but early enough for students to decide if they want to enroll. Thank you for your patience.

Mathematical Sciences Course Catalog Description

A PhD level course that goes deeper into linear programming, starting from where a graduate-level course (5593) ends. Topics include advanced sensitivity analysis, sparse matrix techniques, and special structures. Additional topics, which vary, include deeper analysis of algorithms, principles of model formulation and solution analysis. (Every three years, 3 credit hours)

Instructor Description

In contrast to the introductory course on linear programming (5593) that typically follows its historical development beginning with the simplex method and duality theory before discussing interior-point algorithms, this advanced-level PhD course will take a much more general approach and embed the theory and algorithms of linear programming into the broader class of conic linear programs within convex optimization. Thus starting with a brief review of the fundamentals in polyhedral theory and convex analysis as well as some basic concepts from nonlinear analysis and optimization, the second part of the course will focus primarily on interior-point methods for linear, second-order cone, and semidefinite programs (LP/SOCP/SDPs) while introducing important applications for each of these three problem classes in portfolio optimization, structural engineering, antenna array and filter design, sensor location, signal processing, robust least-squares and norm minimization problems. Taking an excursion into the world of integer programming in the third part, this course will then address LP and SDP relaxations for NP-hard combinatorial optimization problems with applications to maximum-cut, facility layout and location, energy ground states in statistical physics, and the traveling-salesman problem - at which stage the simplex method will finally celebrate its triumphal return to the scene! Last, as time permits, the course will conclude with additional topics of interest to the students including complexity theory, analysis of algorithms, computational efficiency using decomposition and sparse matrix techniques, and other special structures. What sounds fun on paper will be fun in the classroom and include rigorous proofs and the use of freely available and state-of-the-art mathematical programming and optimization software.