Contributed Session Mon.2.H 0107

Monday, 13:15 - 14:45 h, Room: H 0107

Cluster 16: Nonlinear programming [...]

Methods for nonlinear optimization II


Chair: Csizmadia Zsolt



Monday, 13:15 - 13:40 h, Room: H 0107, Talk 1

Art Gorka
Parallel direction finding algorithm in method of feasible directions

Coauthor: Michael Kostreva


A Parallel version of the Method of Feasible Directions algorithm is presented. Parallelization allows for finding multiple directions simultaneously on parallel machines. The algorithm is tested on a number of problems with known solutions from Hock-Schittkowski and compared with sequential algorithms. A numberfold speedup ratios are reported.



Monday, 13:45 - 14:10 h, Room: H 0107, Talk 2

James T. Hungerford
Edge directions in polyhedral optimization

Coauthor: William W. Hager


We consider the problem of maximizing a
continuously differentiable function f(x) over a polyhedron
{P} ⊂ Rn. We present new first and second order
optimality conditions for this problem which are stated
in terms of the derivatives of f along directions parallel
to the edges of {P}. We show that for a special class of
quadratic programs, local optimality can be checked
in polynomial time. Finally, we present a new continuous
formulation for a well known discrete optimization
problem: the vertex separator problem on a graph G.
Easily checked optimality conditions for this problem are
derived via the theory of edge directions. These optimality
conditions are shown to be related to the existence of
edges at specific locations in the graph.



Monday, 14:15 - 14:40 h, Room: H 0107, Talk 3

Csizmadia Zsolt
Pros and cons of first order methods for solving general nonlinear problems


Second order methods to solve non-linear problems are often the best off the shelf methods to solve general non-linear problems due to their robustness and favorable un-tuned convergence properties. However, there are several problem classes, where either due to the special structure of the problem, or their size make first order approaches several magnitudes faster compared to their second order counterparts. First order methods exhibit several well know numerically unfavorable properties; successful applications often rely on efficient, problem specific methods of addressing these challenges. The talk will focus on practical examples and applications where sequential linear programming approaches are either superior, or can be adjusted to achieve significantly better performance than second order methods if the right problem formulation or algorithmic features are used.


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