## Invited Session Fri.2.H 0110

#### Friday, 13:15 - 14:45 h, Room: H 0110

**Cluster 9: Global optimization** [...]

### Algorithms and applications

**Chair: Ernesto G. Birgin**

**Friday, 13:15 - 13:40 h, Room: H 0110, Talk 1**

**Leandro Fonseca Prudente**

An augmented Lagrangian method with finite termination

**Coauthors: Ernesto G. Birgin, José Mario Martínez**

**Abstract:**

We will present a new algorithm based on the Powell-Hestenes-Rockafellar Augmented Lagrangian approach for constrained global optimization. Possible infeasibility will be detected in finite time. Furthermore, we will introduce a pratical stopping criterion that guarantees that, at the approximate solution provided by the algorithm, feasiability holds up to some prescribed tolerance and the objective function value is the optimal one up to tolerance *ε*. At first, in this algoritm, each subproblem is solved with a precision *ε*_{k} that tends to zero. An adaptive modification in which optimality subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows one to detect possible infeasiability without requiring to solve suproblems with increasing precision. In this way, we aim rapid detection of infeasibility, without solving expensive subproblems with unreliable precision.

**Friday, 13:45 - 14:10 h, Room: H 0110, Talk 2**

**Luis Felipe Bueno**

Low order-value approach for solving VaR-constrained optimization problems

**Coauthors: Ernesto G. Birgin, Natasa Krejiç, José Mario Martínez**

**Abstract:**

In low order-value optimization (LOVO) problems the sum of the *r* smallest values of a finite sequence of *q* functions is involved as the objective to be minimized or as a constraint. The latter case is considered in the present paper. Portfolio optimization problems with a constraint on the admissible value-at-risk (VaR) can be modeled in terms of LOVO-constrained minimization. Different algorithms for practical solution of this problem will be presented. Global optimization properties of both the problem and the presented algorithms will be discussed. Using these techniques, portfolio optimization problems with transaction costs will be solved.

**Friday, 14:15 - 14:40 h, Room: H 0110, Talk 3**

**Marina Andretta**

Deterministic and stochastic global optimization techniques for planar covering with elipses problems

**Coauthor: Ernesto G. Birgin**

**Abstract:**

We are interested in the problem of planar covering of points with ellipses: we have a set of *n* demand points in the plane (with weights associated to them), a set of m ellipses (with costs associated to their allocation) and we want to allocate *k* of these ellipses and cover some demand points to get the maximum profit. The profit is measured by summing the weight of the covered demand points and subtracting the costs of the allocated ellipses. Ellipses can have a fixed angle or each of them can be freely rotated. We present deterministic global optimization methods for both cases, while a stochastic version of the method will also be presented for large instances of the latter case. Numerical results show the effectiveness and efficiency of the proposed methods are presented.