Invited Session Wed.3.H 2053

Wednesday, 15:15 - 16:45 h, Room: H 2053

Cluster 9: Global optimization [...]

Nonconvex optimization: Theory and algorithms

 

Chair: Evrim Dalkiran

 

 

Wednesday, 15:15 - 15:40 h, Room: H 2053, Talk 1

Evrim Dalkiran
RLT-POS: Reformulation-linearization technique-based optimization software for polynomial programming problems

Coauthor: Hanif D. Sherali

 

Abstract:

We introduce a Reformulation-Linearization Technique (RLT)-based open-source optimization software for solving polynomial programming problems (RLT-POS). We present algorithms and mechanisms that form the backbone of RLT-POS, including grid-bound-factor constraints and semidefinite cuts, constraint filtering techniques, reduced RLT representations, and bound tightening procedures. When implemented individually, each model enhancement has been shown to significantly improve the performance of the standard RLT procedure. When implemented simultaneously, the coordination between model enhancement techniques becomes critical for an improved performance since special structures in the original formulation may be thus affected. More specifically, we discuss the coordination between (a) bound-grid-factor constraints and semidefinite cuts and (b) constraint filtering techniques and reduced RLT representations. We present computational results using instances from the literature as well as randomly generated problems to demonstrate the improvement over a standard RLT procedure, and we compare the performances of the software packages BARON, SparsePOP, and Couenne with RLT-POS.

 

 

Wednesday, 15:45 - 16:10 h, Room: H 2053, Talk 2

Hong Seo Ryoo
0-1 multilinear programming & LAD patterns

Coauthor: Kedong Yan

 

Abstract:
In this paper, we present a new framework for generating LAD patterns based on 0-1 multilinear programming. The new framework is useful in that one can apply standard linearization techniques and obtain all optimization/MILP-based pattern generation models that have been developed in the literature. We demonstrate this and then apply the McCormick’s relaxation and logical implications to develop new pattern generation models that involve a small number of 0-1 decision variables and constraints. With experiments on benchmark machine learning datasets, we demonstrate the efficiency of the new MILP models over previously developed ones.

 

 

Wednesday, 16:15 - 16:40 h, Room: H 2053, Talk 3

Spencer D. Schaber
Convergence order of relaxations for global optimization of nonlinear dynamic systems

Coauthor: Paul I. Barton

 

Abstract:
Deterministic methods for global optimization of nonlinear dynamic systems rely upon underestimating problems for rigorous bounds on the objective function on subsets of the search space. Convergence order of numerical methods is frequently highly indicative of their computational requirements, but has not yet been analyzed for these methods. We analyzed the convergence order of the underestimating problems to the original nonconvex problem for one method of nonlinear global dynamic optimization. We found that the convergence order of the underestimating problem is bounded below by the smallest of the convergence orders of the methods used to compute (i) the bounds for the states as well the convex/concave relaxations of the (ii) vector field, (iii) initial condition, and (iv) objective function in terms of the state variables. We compared the theoretical convergence order result to empirical results for several optimal-control and parameter-estimation problems and found that the bounds were valid for all problems and sharp for some. We confirmed that empirical convergence order is highly correlated with the CPU time for full global dynamic optimization.

 

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