TE-04: Advanced Optimization Methods I
Stream: Advanced Optimization Methods
Room: Lagrange
Chair(s): Marat Mukhametzhanov

Reduced-Order Parameter Optimization by Sequential ALIENOR method
Daniele Peri
Space Filling Curves (SFC) are a class of curves that completely covers a portion of a N-dimensional space asymptotically: an arbitrary position of the space is then associated with a single parameter (the curved abscissa along the SFC). This way, an N dimensional optimization problem can be converted in a 1D problem (ALIENOR method). In this paper a sequential approach using SFC is presented, managing hundreds of design variables: solution is obtained by iterativerly focusing on smaller and smaller portions of the feasible set. An industrial application is also presented.

Univariate Lipschitz Global Optimization Methods for Finding the Shape Parameter Value in Radial Basis Functions
Marat Mukhametzhanov, Yaroslav Sergeyev
Radial basis function (RBF) interpolation is considered in this talk. It is well-known that the value of the shape parameter of the RBFs has a strong impact on both the accuracy and stability of the results. It has been proposed recently to use univariate Lipschitz global optimization methods for finding an optimal value of the parameter. Locally-biased versions of the well-known “Divide-the-best” algorithms are presented for this purpose. Numerical experiments on several randomized and real-life test problems show the advantages of proposed the techniques.

On a new shape derivative formula based approach for a shape optimization problem with constrained coupled problems
Azeddine SADIK, Abdesslam BOULKHEMAIR, Abdelkrim CHAKIB
In this paper, we deal with numerical method for the approximation of a class of coupled shape optimization problem, which consist in minimizing an appropriate general cost functional subjected to coupled boundary value problems by means of a Neumann boundary transmission condition. We show the existence of the shape derivative of the cost functional and express it by means of support functions. Then the numerical discretization is performed using the dual reciprocity boundary element method. Finally, we give some numerical results,showing the efficiency of the proposed approach.

Piecewise Linear Bounding of the Euclidean Norm
Aloïs Duguet, Christian Artigues, Laurent houssin, Sandra Ulrich Ngueveu
In the field of piecewise linear approximation of nonlinear functions, few studies focused on the minimization of the number of pieces for a given error bound. In this talk we focus on the euclidean norm defined on a plane, and we first show how to use scalar products with regularly spaced unit vectors in order to compute piecewise linear approximations with the minimum number of pieces for a given relative error bound. Then we extend the approach to norms with elliptic level sets. An application to the beam layout problem validates the tractability of the method.