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Type of Document Dissertation Author Lin, Youdong Author's Email Address ylin@nd.edu URN etd-07062004-160554 Title LP-BASED STRATEGIES FOR DETERMINISTIC GLOBAL OPTIMIZATION USING INTERVAL METHODS Degree Doctor of Philosophy Department Chemical Engineering Advisory Committee
Advisor Name Title Mark Stadtherr Committee Member Keywords
- global optimization
- interval analysis
- linear programming
Date of Defense 2004-06-29 Availability mixed Abstract The interval Newton method can provide mathematical and computationalguarantee that all roots will be found in nonlinear equation
solving problems, and that the global optimum will be found in
nonlinear, nonconvex optimization problems.
Thus this provides a methodology for deterministic global
optimization, including the problem of finding all stationary points
in unconstrained optimization, or all Fritz-John points in constrained
optimization.
We present here a new strategy based on the use of linear programming
(LP) techniques to exactly (within round out)
bound the solution set of the linear interval
equation system that must be solved in the context of the
interval-Newton method. The tighter bound on solution set thus
enhances
may greatly enhance the
efficiency of the
interval-Newton method.
An implementation of this technique is
described and several important issues are considered.
These include combination with a simple, low-overhead pivoting
preconditioning technique, selection of the interval conner required
by the LP strategy, and determination of rigorous bounds on the
solution of the LP problems. The procedure based on these techniques,
LISS_LP, will then be demonstrated using several global optimization
problems, with focus on problems arising in chemical engineering.
The comparative computational performance results between LISS_LP and
the HP/RP approach of Gau and Stadtherr, have shown that
the new LP strategy leads to substantial reductions in computation
time requirements.
In addition, LISS_LP has also been applied to some global optimization
problems arising in molecular modeling, such as
locating all stationary points of the potential energy surface of a
sorbate particle in silicalite,
locating all stationary points of the potential energy surface of
triatomic molecules,
and seeking molecular conformation with global minimum potential energy.
It has been shown that the new LP-based strategy for the interval
Newton method implemented in LISS_LP,
is very effective on these problems.
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