search

UMD     This Site





Professor AndréTits (ECE/ISR) is the co-principal investigator for a new Department of Energy (DoE) grant, ?Interior-Point Algorithms for Optimization Problems with Many Constraints.? The Principal Investigator for this grant is Professor Dianne O?Leary (CS/UMIACS). The three-year, $303,701 grant continues the research of an earlier grant in the same area.

About the research
The researchers will develop, analyze, and test algorithms for the solution of optimization problems with a very large number of inequality constraints, specifically, many more inequality constraints than variables. These types of problems arise, for example, in support vector machine training (for classification of data), network problems, and fine discretizations of semi-infinite programming problems such as those arising from partial differential equation models.

The researchers will consider problems related to linear programming (LP), convex or indefinite quadratic programming, and convex programming, as well as more general nonlinear programming.

Under the earlier grant, the PIs and their collaborators developed a framework for constraint reduction. For LP (i.e., minimization/maximization of a linear function subject to linear constraints), the idea is as follows. The solution of an LP is entirely determined by its objective function and a subset of the constraints, usually of size equal to the number of variables. Accordingly if the number of inequality constraints is much larger than the number of variables, then most of the constraints are, in a sense, irrelevant. Unfortunately, it is unknown at the outset which these are. This is what makes an LP hard to solve.

The framework already developed by AndréTits and Dianne O?Leary adaptively identifies, at each iteration of the solution process, a small set of seemingly critical constraints, and determines a search direction based on those constraints only. The algorithm was validated by theoretical analysis and numerical experimentation for linear and quadratic programming.

This new grant will allow the researchers to:

?Investigate approaches to efficiently deal with situations when the problem is ?sparse" (i.e., each variable is involved in only a small number of constraints);

?Improve the performance of algorithms to train support-vector machines, used for classifying data;

?Extend the work to general nonlinear programming (problems with nonlinear constraints); and

?Apply the techniques to entropy-based moment closure in gas dynamics.

Applications
As has been the case with previous algorithms and software developed by AndréTits and his coauthors (CFSQP, FFSQP, RFSQP and a number of Matlab scripts), the algorithms and software that will come out of the proposed research should have a significant impact in a wide range of application areas. This includes many areas of engineering (chemical, mechanical, electrical, transportation, controls...), but also areas such as medical research (epidemiology, oncology, radiology), statistics, finance and astronomy.

The work already completed under the earlier grant has had many connections to DoE labs; the new grant should produce algorithms and software of use to DoE as well as to the broader community. For example, algorithms to train SVMs could help detect anomalies in network interactions for homeland security, identify specific genome features, find supernovae, and estimate direction-of-arrival in signal processing.



Related Articles:
When does a package delivery company benefit from having two people in the truck?
Al-Obaid, Adomaitis publish renewable energy algorithm in Royal Society of Chemistry journal
S. Raghu Raghavan is a runner-up for INFORMS Computing Society Prize
Michael Fu part of $1M NSF grant to model, disrupt illicit kidney trafficking networks
Alexander Estes joins ISR faculty
Alum Marcos Vasconcelos to join FSU faculty this fall
In Memoriam: 'Advisor for Life' Pravin Varaiya
Fatemeh Alimardani receives WTS-DC scholarship
Michael Fu part of NSF project to improve kidney transplant access and decision-making
Hybrid inverse optimization can help in modeling natural disaster responses

September 28, 2009


«Previous Story  

 

 

Current Headlines

UMD Launches Institute Focused on Ethical AI Development

Remembering Rance Cleaveland (1961-2024)

Dinesh Manocha Inducted into IEEE VGTC Virtual Reality Academy

ECE Ph.D. Student Ayooluwa (“Ayo”) Ajiboye Recognized at APEC 2024

Balachandran, Cameron, Yu Receive 2024 MURI Award

UMD, Booz Allen Hamilton Announce Collaboration with MMEC

New Research Suggests Gossip “Not Always a Bad Thing”

Ingestible Capsule Technology Research on Front Cover of Journal

Governor’s Cabinet Meeting Features Peek into Southern Maryland Research and Collaboration

Celebrating the Impact of Black Maryland Engineers and Leaders

 
 
Back to top  
Home Clark School Home UMD Home