ICS »

Stream: Derivative-free optimization

Chair: Stefano Lucidi

1. On subdivision strategies in DIRECT-type algorithms
   Julius Žilinskas, Remigijus Paulaviˇcius
   
   
   

   The well known DIRECT algorithm for global optimization is based on dividing hyper-rectangles and evaluating objective function at the centers. Various modifications have been proposed including the use of simplices instead of rectangles, sampling more than one point on diagonal or vertices, etc. In order to use the sampled function value in descendant partitions a trisection is often used, but new subdivision strategies allow bisection which is preferable because of resulting shapes. In this talk we discuss and compare various sampling and subdivision strategies.
   
   

2. A linesearch derivative-free method with adaptive precision function evaluations and application to bilevel minimization problems
   Stefano Lucidi, Stefania Renzi
   
   
   

   In this work we propose a new linesearch derivative-free algorithm for nonsmooth optimization problems with adaptive precision function evaluations. Under suitable assuptions we prove that an accumulation point of the sequence produced by the algorithm is a Clarke-stationary point of the considered problem. Then the proposed method is applied for solving a particular class of bilevel minimization problems. Finally we report the results of a preliminary numerical experience showing a possible practical interest of the proposed approach.
   
   

3. Probabilistic feasible descent techniques for derivative-free linearly constrained optimization
   Clément Royer, Serge Gratton, Luis Nunes Vicente, Zaikun Zhang
   
   
   

   We describe a direct-search scheme for linearly constrained optimization, based on randomly generated directions that guarantee probabilistic feasible descent, in a generalization from a recent unconstrained study. By applying martingale-type arguments to assess the quality of the directions used throughout the algorithm, we establish global convergence with probability one as well as convergence rates with overwhelming probability. Such complexity bounds indicate possible interesting gains over deterministic solvers, a prospect supported by preliminary numerical experience.