Contributed Session Thu.3.H 2053

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

Cluster 9: Global optimization [...]

Advances in global optimization III


Chair: Duy Van Nguyen



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

Tibor Csendes
Symbolic simplification of nonlinear optimization problems

Coauthor: Elvira Antal


We present a Maple implementation of a symbolic algorithm that is capable to transform the original nonlinear global optimization problem into an equivalent form, that is simpler in the sense that it has less operations to be calculated. The algorithm can also recognize redundancy in the optimized variables, and in this sense it can decrease the dimensionality of the problem (if it is possible). The applied transformations can preserve the number of local minimizer points, and the solution of the transformed problem can easily be transformed back to the space of the original variables.
We have tested the code on the set of standard global optimization problems and on some custom made simplifiable problems. The results are convincing in terms that the algorithm concluded in almost all cases according to our knowledge on the problems.

Csendes, T. and T. Rapcsák: Nonlinear Coordinate Transformations for Unconstrained Optimization. I. Basic Transformations, J. of Global Optimization 3(1993) 213-221.



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

Chu Ngoc Nguyen
The interior exterior approach for linear programming problem

Coauthors: Nguyen Ngoc Chu, Pham Canh Duong, Le Thanh Hue


In this paper we present a new interior exterior algorithm for solving linear programming problem which can be viewed as a variation of simplex method in combination with interior approach. With the assumption that a feasible interior solution to the input system is known, this algorithm uses it and appropriate constraints of the system to construct a sequence of the so called station cones whose vertices tend very fast to the solution to be found. The computational experiments show that the number of iterations of the interior exterior algorithm is significantly smaller than that of the second phase of the simplex method. Additionally, when the number of variables and constraints of the problem increase, the number of iterations of the interior exterior approach increase in a slower manner than that of the simplex method.



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

Duy Van Nguyen
Solving standard problem (StQP)


We consider the standard quadratic problem (StQP) which consists of globally minimizing
an indefinite quadratic function over the simplex. We propose a
a finite but exponential solution algorithm in which the main task of each iteration is to
check semidefiniteness of a k × k symmetric matrix with k ≤ n. We show some
illustrative examples and computational test results for the algorithm.


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