Title:
Mixed integer programming approaches for nonlinear and stochastic programming

Simple item page
dc.contributor.advisor Nemhauser, George L.
dc.contributor.advisor Ahmed, Shabbir
dc.contributor.author Vielma Centeno, Juan Pablo en_US
dc.contributor.committeeMember Cook, William J.
dc.contributor.committeeMember Gu, Zonghao
dc.contributor.committeeMember Johnson, Ellis L.
dc.contributor.department Industrial and Systems Engineering en_US
dc.date.accessioned 2009-08-26T17:31:46Z
dc.date.available 2009-08-26T17:31:46Z
dc.date.issued 2009-07-06 en_US
dc.description.abstract In this thesis we study how to solve some nonconvex optimization problems by using methods that capitalize on the success of Linear Programming (LP) based solvers for Mixed Integer Linear Programming (MILP). A common aspect of our solution approaches is the use, development and analysis of small but strong extended LP/MILP formulations and approximations. In the first part of this work we develop an LP based branch-and-bound algorithm for mixed integer conic quadratic programs. The algorithm is based on a lifted polyhedral relaxation of conic quadratic constraints by Ben-Tal and Nemirovski. We test the algorithm on a series of portfolio optimization problems and show that it provides a significant computational advantage. In the second part we study the modeling of a class of disjunctive constraints with a logarithmic number of variables. For specially structured disjunctive constraints we give sufficient conditions for constructing MILP formulations with a number of binary variables and extra constraints that is logarithmic in the number of terms of the disjunction. Using these conditions we introduce formulations with these characteristics for SOS1, SOS2 constraints and piecewise linear functions. We present computational results showing that they can significantly outperform other MILP formulations. In the third part we study the modeling of non-convex piecewise linear functions as MILPs. We review several new and existing MILP formulations for continuous piecewise linear functions with special attention paid to multivariate non-separable functions. We compare these formulations with respect to their theoretical properties and their relative computational performance. In addition, we study the extension of these formulations to lower semicontinuous piecewise linear functions. Finally, in the fourth part we study the strength of MILP formulations for LPs with Probabilistic Constraints. We first study the strength of existing MILP formulations that only considers one row of the probabilistic constraint at a time. We then introduce an extended formulation that considers more than one row of the constraint at a time and use it to computationally compare the relative strength between formulations that consider one and two rows at a time. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/29624
dc.publisher Georgia Institute of Technology en_US
dc.subject Mixed integer programming en_US
dc.subject.lcsh Stochastic programming
dc.subject.lcsh Mathematical optimization
dc.subject.lcsh Nonconvex programming
dc.title Mixed integer programming approaches for nonlinear and stochastic programming en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Nemhauser, George L.
local.contributor.corporatename H. Milton Stewart School of Industrial and Systems Engineering
local.contributor.corporatename College of Engineering
relation.isAdvisorOfPublication cc31c1dc-5388-470a-9c3f-f8976a299674
relation.isOrgUnitOfPublication 29ad75f0-242d-49a7-9b3d-0ac88893323c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
vielma_centeno_juan_pablo_200908_phd.pdf
Size:
1.71 MB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Theses and Dissertations