Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
On generalized bisection of n-simplices
Mathematics of Computation
Stochastic algorithms in nonlinear regression
Computational Statistics & Data Analysis
Using DIRECT to Solve an Aircraft Routing Problem
Computational Optimization and Applications
A Locally-Biased form of the DIRECT Algorithm
Journal of Global Optimization
A Comparison of Global Optimization Methods for the Design of a High-speed Civil Transport
Journal of Global Optimization
Dynamic Data Structures for a Direct Search Algorithm
Computational Optimization and Applications
Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants
SIAM Journal on Optimization
Additive Scaling and the DIRECT Algorithm
Journal of Global Optimization
Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Infeasibility spheres for finding robust solutions of blending problems with quadratic constraints
Journal of Global Optimization
Computational Optimization and Applications
A partition-based global optimization algorithm
Journal of Global Optimization
Lipschitz gradients for global optimization in a one-point-based partitioning scheme
Journal of Computational and Applied Mathematics
A hybrid global optimization algorithm for non-linear least squares regression
Journal of Global Optimization
A modification of the DIRECT method for Lipschitz global optimization for a symmetric function
Journal of Global Optimization
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In this paper we propose a new simplicial partition-based deterministic algorithm for global optimization of Lipschitz-continuous functions without requiring any knowledge of the Lipschitz constant. Our algorithm is motivated by the well-known Direct algorithm which evaluates the objective function on a set of points that tries to cover the most promising subregions of the feasible region. Almost all previous modifications of Direct algorithm use hyper-rectangular partitions. However, other types of partitions may be more suitable for some optimization problems. Simplicial partitions may be preferable when the initial feasible region is either already a simplex or may be covered by one or a manageable number of simplices. Therefore in this paper we propose and investigate simplicial versions of the partition-based algorithm. In the case of simplicial partitions, definition of potentially optimal subregion cannot be the same as in the rectangular version. In this paper we propose and investigate two definitions of potentially optimal simplices: one involves function values at the vertices of the simplex and another uses function value at the centroid of the simplex. We use experimental investigation to compare performance of the algorithms with different definitions of potentially optimal partitions. The experimental investigation shows, that proposed simplicial algorithm gives very competitive results to Direct algorithm using standard test problems and performs particularly well when the search space and the numbers of local and global optimizers may be reduced by taking into account symmetries of the objective function.