Second-Order Convergence of Mesh-Adaptive Direct Search
نویسندگان
چکیده
Abstract: A previous analysis of second-order behavior of pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search (MADS) algorithms for general constrained optimization. Because of the ability of MADS to generate an asymptotically dense set of search directions, we are able to establish reasonable conditions under which a subsequence of MADS iterates converges to a limit point satisfying second-order necessary or sufficient optimality conditions for general set-constrained optimization problems.
منابع مشابه
Convergence of Mesh Adaptive Direct Search to Second-Order Stationary Points
A previous analysis of second-order behavior of generalized pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more general class of mesh adaptive direct search (MADS) algorithms for general constrained optimization. Because of the ability of MADS to generate an asymptotically dense set of search directions, we are able to establish reasonable c...
متن کاملUse of quadratic models with mesh-adaptive direct search for constrained black box optimization
We consider derivative-free optimization, and in particular black box optimization, where the functions to minimize and the functions representing the constraints are given by black boxes without derivatives. Two fundamental families of methods are available: Model-based methods and directional direct search algorithms. This work exploits the flexibility of the second type of method in order to...
متن کاملNonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search
This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm, which extends the Generalized Pattern Search (GPS) algorithm, with the Variable Neighborhood Search (VNS) metaheuristic, for nonsmooth constrained optimization. The resulting algorithm retains the convergence properties of MADS, and allows the far reaching exploration features of VNS to move away from local s...
متن کاملNonlinear programming by mesh adaptive direct searches
This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitations dictate a brief description of various key topics to be provided along with several references, which themselves provide further references. The convergence theory for the methods presented here make a case for closing the gap between non...
متن کاملParallel Space Decomposition of the Mesh Adaptive Direct Search Algorithm
This paper describes a Parallel Space Decomposition (PSD) technique for the Mesh Adaptive Direct Search (MADS) algorithm. MADS extends Generalized Pattern Search for constrained nonsmooth optimization problems. The objective here is to solve larger problems more efficiently. The new method (PSD-MADS) is an asynchronous parallel algorithm in which the processes solve problems over subsets of var...
متن کامل