Global Optimization in Action—Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications

By J. Pintér. 2010

314 citations recorded by the source corpus.

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Adaptive nested optimization scheme for multidimensional global search (2015, methodology): “This approach is close to univariate scheme of characteristical algorithms [11] and the methods based on multidimensional partitioning are presented, for instance, in [17,19–24].”
Aggregation Functions: A Guide for Practitioners (2007, methodology): “Even if the class of the objective functions is limited to smooth or Lipschitz functions, the global optimization problem is NP-hard [128, 129, 130, 204].”
From Bandits to Monte-Carlo Tree Search: The Optimistic Principle Applied to Optimization and Planning (2014, methodology): “A large body of algorithmic work has been developed using branch-and-bound techniques [94, 67, 79, 71, 98, 57, 110] such as Lipschitz optimization where the function is assumed to be globally Lipschitz.”
Derivative-free optimization: a review of algorithms and comparison of software implementations (2012, background): “TOMLAB/LGO [107]: a suite of global and local nonlinear solvers [106] that implements a combination of Lipschitzian-based branch-and-bound with deterministic and stochastic local search (several versions of LGO are available, for instance under Maple, and may offer different features than TOMLAB/LGO”
A literature survey of benchmark functions for global optimisation problems (2013, unknown): “Pintér Function [63] (Continuous, Differentiable, Non-separable, Scalable, Multimodal) f89(x) = D ∑”