Derivative-free algorithms are frequently required for the optimization of nonsmooth scalar functions in n dimensions resulting, for example, from physical experiments or from the statistical averaging of numerical simulations of chaotic systems such as turbulent flows. The core idea of all...

A function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${f : \Omega \to \mathbb{R}}$$</EquationSource> </InlineEquation> , where Ω is a convex subset of the linear space X, is said to be d.c. (difference of convex) if f =  g − h with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${g, h : \Omega \to \mathbb{R}}$$</EquationSource> </InlineEquation> convex functions. While d.c. functions find various applications, especially in optimization, the...</equationsource></inlineequation></equationsource></inlineequation>

In previous work, Costa and Alves (J Math Sci 161:(6)820–831, <CitationRef CitationID="CR2">2009</CitationRef>; <CitationRef CitationID="CR3">2011</CitationRef>) have presented Branch & Bound and Branch & Cut techniques that allow for the effective computation of nondominated solutions, associated with reference points, of multi-objective linear fractional programming (MOLFP)...</citationref></citationref>

A large number of problems in ab-initio quantum chemistry involve finding the global minimum of the total system energy. These problems are traditionally solved by numerical approaches equivalent to local optimization. While these approaches are relatively efficient, they do not provide...

In this paper, utilizing the properties of the generalized f -projection operator and the well-known KKM and Kakutani–Fan–Glicksberg theorems, under quite mide assumptions, we derive some new existence theorems for the generalized set-valued mixed variational inequality and the generalized...

This paper introduces the global mixed-integer quadratic optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\varepsilon}$$</EquationSource> </InlineEquation>-global optimality. The algorithmic components are presented for: reformulating user input, detecting...</equationsource></inlineequation>

In this paper we deal with a class of non-differentiable functionals defined on a real reflexive Banach space X and depending on a real parameter of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{E}_\lambda(u)=L(u)-(J_1\circ T)(u)-\lambda (J_2\circ S)(u)}$$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${L:X \rightarrow \mathbb R}$$</EquationSource> </InlineEquation> is a sequentially...</equationsource></inlineequation></equationsource></inlineequation>

Given an undirected network G(V, E, c) and a perfect matching M <Superscript>0</Superscript>, the inverse maximum perfect matching problem is to modify the cost vector as little as possible such that the given perfect matching M <Superscript>0</Superscript> can form a maximum perfect matching. The modification can be measured by different norms. In...</superscript></superscript>

We present the AQUARS (A QUAsi-multistart Response Surface) framework for finding the global minimum of a computationally expensive black-box function subject to bound constraints. In a traditional multistart approach, the local search method is blind to the trajectories of the previous local...

The primary goal of this work is to address the non-linear programming problem of globally minimizing the real valued function x → d(x, Tx) where T is presumed to be a non-self mapping that is a generalized proximal contraction in the setting of a metric space. Indeed, an iterative algorithm...