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Surface passivation optimization using DIRECT

“…The three-dimensional images were produced with the molecular visualization program Visual Molecular Dynamics (VMD) [14]. This work used computing resources at the NREL Computational Sciences Center and is supported by the US DOE-SC-ASCR-Mathematical, Information and The objective function ('Function') is the average percentage of the VBM and CBM wave function contained in the core of the five test structures.…”

Univariate geometric Lipschitz global optimization algorithms

“…Naturally, balancing between local and global information must be performed in an appropriate way (see, e.g., [101,96,113]) since an excessive unjustified usage of local information can lead to the loss of the global solution (see, e.g., [110]). Finally, multiple estimates of L can be chosen during the search from a certain set of admissible values from zero to infinity (see, e.g., [34,40,49,56,95,96]).…”

“…Since during the search it uses a set of possible estimates of L and does not use its single overestimate, only the so-called everywhere dense convergence (i.e., convergence of the sequence of trial points to any point of the search interval) can be established for this method; it is also difficult to apply for the DIRECT some meaningful stopping criterion, such as, for example, stopping on achieving a desired accuracy in solution. Nevertheless, due to its relative simplicity and a satisfactory performance on several test functions and applied problems, the DIRECT has been widely adopted in practical applications (see, e.g., [10,15,17,23,39,49,66,75,120]) and has attracted the attention of the researchers (for its theoretical and experimental analysis and several modifications see, e.g., [22,23,34,40,49,56,65,95]).…”

Derivative-free global ship design optimization using global/local hybridization of the DIRECT algorithm

“…The objective of the present study is the efficient solution of problem (1) by hybridization of DIRECT-type algorithms [19,11,38,1,15,5,12,23,18,13,14,6], which are well-behaved deterministic algorithms for global optimization and have been successfully applied to solve diverse real-world problems. Specifically, the focus is on the DIRMIN algorithm (proposed in [23] and, in a derivative-free context, in [24]) which is an enriched version of the DIRECT algorithm by local minimization.…”