An always convergent algorithm for global mini- mization of univariate Lipschitz functions

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

A univariate global search working with a set of Lipschitz constants for the first derivative

In the paper, a global optimization problem is considered where the objective function f(x) is univariate, black-box, and its first derivative f (x) satisfies the Lipschitz condition with an unknown Lipschitz constant K. In the literature, there exist methods solving this problem by using an a priori given estimate of K, its adaptive estimates, and adaptive estimates of local Lipschitz constant...

Ant Colony Optimization for Multi-objective Digital Convergent Product Network

Convergent product is an assembly shape concept integrating functions and sub-functions to form a final product. To conceptualize the convergent product problem, a web-based network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is considered to be a link between two nodes. The aim is to find an optimal tree of functionali...

Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants

In this paper, the global optimization problem miny∈S F (y) with S being a hyperinterval in R and F (y) satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function F (y) can be multiextremal, non-differentiable, and given as a ‘black-box’. To attack the problem, a new global optimization algorithm based on the following two ideas is prop...

Particle swarm optimization for a bi-objective web-based convergent product networks

Here, a collection of base functions and sub-functions configure the nodes of a web-based (digital)network representing functionalities. Each arc in the network is to be assigned as the link between two nodes. The aim is to find an optimal tree of functionalities in the network adding value to the product in the web environment. First, a purification process is performed in the product network ...