An algorithm for finding the absolute extremum of a function

By S. A. Piyavskii. 1972

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Citations in the corpus

Reachability Analysis of Deep Neural Networks with Provable Guarantees (2018, background): “Inspired by an idea from optimisation, see e.g., [24, 25], we design another continuous function h ( x, y ) , which serves as a lower bound of the original function w ( x ) .”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “) In 1972, Piyavskii [272] introduced complete global optimization methods based on Lipschitz constants, which are in flavor similar to interval methods.”
Application of Bayesian approach to numerical methods of global and stochastic optimization (1994, methodology): “Some optimal in a minimax sense methods were developed also for a set of Lifschitzian functions, see Evtushenko (1985), Pijavskij (1972) , Shubert (1972), Sucharev (1975).”
Global optimization of expensive black box functions using potential Lipschitz constants and response surfaces (2015, methodology): “To speed up the convergence of the standard Lipschitzian algorithm [3,13], Jones et al.”
Adaptive nested optimization scheme for multidimensional global search (2015, methodology): “The scheme (4)–(6) in the case of the Lipschitzian one-dimensional functions φ̃i combined with the one-dimensional algorithms [7,25,32,34–36] has served as the basis for designing a number of the multidimensional methods [3,12,25,26,36].”
Aggregation Functions: A Guide for Practitioners (2007, methodology): “If the objective function is known to be Lipschitz-continuous, and an estimate of its Lipschitz constant M is available, Pijavski-Shubert method [203, 223] is an efficient way to find and confirm the global optimum.”
A Global Maximum Power Point Tracking Scheme Employing DIRECT Search Algorithm for Photovoltaic Systems (2010, methodology): “In this manner, one can develop an efficient algorithm tofind a solution within a prespecified tolerance of an optimal solution in a finite number of iterations [ 21 ], [22].”