Nonsmooth optimization through Mesh Adaptive Direct Search and Variable Neighborhood Search
Journal of Global Optimization
Algorithm 909: NOMAD: Nonlinear Optimization with the MADS Algorithm
ACM Transactions on Mathematical Software (TOMS)
Combined heat and power economic dispatch by mesh adaptive direct search algorithm
Expert Systems with Applications: An International Journal
Structural and Multidisciplinary Optimization
Direct search algorithm for bilevel programming problems
Computational Optimization and Applications
Structural and Multidisciplinary Optimization
Computers and Operations Research
Journal of Global Optimization
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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 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.