Thesis Defense :: Global Optimization of Monotonic Programs: Applications in Polynomial and Stochastic Programming

Event Details
  • Date/Time:
    • Monday April 11, 2005
      10:00 am - 12:00 am
  • Location: Groseclose Building, Room 403
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Contact
Barbara Christopher
Industrial and Systems Engineering
Contact Barbara Christopher
404.385.3102
Summaries

Summary Sentence: Thesis Defense :: Global Optimization of Monotonic Programs: Applications in Polynomial and Stochastic Programming

Full Summary: Thesis Defense :: Global Optimization of Monotonic Programs: Applications in Polynomial and Stochastic Programming

Monotonic optimization consists of minimizing or maximizing a monotonic objective function over a set of constraints defined by monotonic functions. Many optimization problems in economics and engineering often have monotonicity while lacking other useful properties, such as convexity. This thesis in concerned with the development and application of global optimization algorithms for monotonic optimization problems.

First, we propose enhancements to an existing outer-approximation algorithm -- called the Polyblock algorithm -- for monotonic optimization problems. The enhancements are shown to significantly improve the computational performance of the algorithm while retaining the convergence properties. Next, we develop a generic branch-and-bound algorithm for monotonic optimization problems. A computational study is carried out for comparing the performance of the Polyblock algorithm and variants of the proposed branch-and-bound scheme on a family of separable polynomial programming problems. Finally, we study an important class of monotonic optimization problems -- probabilistically constrained linear programs. We develop a branch and bound algorithm that searches for a global solution to the problem. The basic algorithm is enhanced by domain reduction and cutting plane strategies to reduce the size of the partitions and hence tighten bounds. The proposed branch-reduce-cut algorithm exploits the monotonicity properties inherent in the problem, and requires solving linear programming subproblems. We provide convergence proofs for the algorithm. Some illustrative numerical results involving problems with discrete distributions are presented.

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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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Status
  • Created By: Barbara Christopher
  • Workflow Status: Published
  • Created On: Oct 8, 2010 - 7:38am
  • Last Updated: Oct 7, 2016 - 9:52pm