Mixed Integer Nonlinear Programs: Theory, Algorithms and Applications
Tawarmalani, Mohit
This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.
Permalink
https://hdl.handle.net/2142/87075
Description
Title
Mixed Integer Nonlinear Programs: Theory, Algorithms and Applications
Author(s)
Tawarmalani, Mohit
Issue Date
2001
Doctoral Committee Chair(s)
Sahinidis, Nikolaos V.
Department of Study
Industrial Engineering
Discipline
Industrial Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
This dissertation develops an efficient solution strategy for finding global optima of continuous, integer, and mixed integer nonlinear programs. The main contributions of this thesis are: (1) We develop the first constructive technique for characterizing convex envelopes of nonlinear functions. Demonstrating the technique, we derive a semidefinite relaxation for fractional programs. In the process, we introduce the concept of convex extensions, study its convexification properties, and apply it to develop tight relaxations for hyperbolic programs and pooling/blending problems. (2) We develop a theoretical framework for range-reduction and provide a unified treatment of existing and new domain reduction techniques. (3) We develop a finite algorithm for two stage stochastic integer programs where earlier approaches were either convergent only in limit (i.e., infinite) or resorted to explicit enumeration. (4) We provide computational experience to demonstrate that our implementation of the proposed algorithms (BARON-NLP) can routinely solve problems previously not amenable to optimization techniques. We characterize the feasible space of a refrigerant design problem proposed 15 years ago and provide new solutions and/or improved computational results with respect to earlier approaches on benchmark problems in stochastic decision making, pooling and blending problems in the petrochemical industry, and restaurant location problems.
Use this login method if you
don't
have an
@illinois.edu
email address.
(Oops, I do have one)
IDEALS migrated to a new platform on June 23, 2022. If you created
your account prior to this date, you will have to reset your password
using the forgot-password link below.
