## 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**

**Abstract:**

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.

\noindent

Csendes, T. and T. RapcsĂˇk: 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**

**Abstract:**

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)

**Abstract:**

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.