DOI

10.17077/etd.a72hyjg2

Document Type

Dissertation

Date of Degree

Spring 2017

Degree Name

PhD (Doctor of Philosophy)

Degree In

Civil and Environmental Engineering

First Advisor

Arora, Jasbir S.

Second Advisor

Abdel-Malek, Karim

First Committee Member

Rahmatalla, Salam

Second Committee Member

Bhatti, Asghar

Third Committee Member

Bhatt, Rajan

Abstract

A new optimization algorithm, which can efficiently solve large-scale constrained non-linear optimization problems and leverage parallel computing, is designed and studied. The new algorithm, referred to herein as LASO or LArge Scale Optimizer, combines the best features of various algorithms to create a computationally efficient algorithm with strong convergence properties. Numerous algorithms were implemented and tested in its creation. Bound-constrained, step-size, and constrained algorithms have been designed that push the state-of-the-art. Along the way, five novel discoveries have been made: (1) a more efficient and robust method for obtaining second order Lagrange multiplier updates in Augmented Lagrangian algorithms, (2) a method for directly identifying the active constraint set at each iteration, (3) a simplified formulation of the penalty parameter sub-problem, (4) an efficient backtracking line-search procedure, (5) a novel hybrid line-search trust-region step-size calculation method. The broader impact of these contributions is that, for the first time, an Augmented Lagrangian algorithm is made to be competitive with state-of-the-art Sequential Quadratic Programming and Interior Point algorithms.

The present work concludes by showing the applicability of the LASO algorithm to simulate one step of digital human walking and to accelerate the optimization process using parallel computing.

Public Abstract

Numerical optimization is a fundamental and necessary step in the simulation of many real-world processes in the sciences, physics, engineering, and economics. Unfortunately, however, the sequential nature of the optimization process often acts as one of the greatest bottlenecks to achieving real-time simulation in these fields. One such example, which is considered here, is the problem of digital human simulation. Therefore, a new optimization algorithm and associated software package, which can efficiently solve large-scale problems and leverage parallel computing, is needed. The result of this research is a new optimization algorithm and general purpose software package that push the state-of-the-art in the field of optimization.

Keywords

Augmented Lagrangian, Digital Human Simulation, Interior Point, L-BFGS, Optimization, Sequential Quadratic Programming (SQP)

Pages

xiv, 121 pages

Bibliography

Includes bibliographical references (pages 103-107).

Copyright

Copyright © 2017 John Corbett Nicholson

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