The Standard Quadratic Problem (StQP) is an NP-hard problem with many local minimizers (stationary points). In the literature, heuristics based on unconstrained continuous non-convex formulations have been proposed (Bomze & Palagi, 2005; Bomze, Grippo, & Palagi, 2012) but none dominates the other in...

In this paper a solution algorithm for a class of rank-two nonconvex programs having a polyhedral feasible region is proposed. The algorithm is based on the so called optimal level solutions method. Various global optimality conditions are discussed and implemented in order to improve the...

In this paper a solution algorithm for a class of rank-two nonconvex programs having a polyhedral feasible region is proposed. The algorithm is based on the so called optimal level solutions method. Various global optimality conditions are discussed and implemented in order to improve the...

Several numerical methods for solving nonlinear systems of equations assume that derivative information is available. Furthermore, these approaches usually do not consider the problem of finding all solutions to a nonlinear system. Rather, most methods output a single solution. In this paper, we...

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$[\bar{l}, \bar{u}]$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">[</mo> <mover accent="true"> <mrow> <mi>l</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo>,</mo> <mover accent="true"> <mrow> <mi>u</mi> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo stretchy="false">]</mo> </mrow> </math> </EquationSource> </InlineEquation> in such a way that, in...</equationsource></equationsource></inlineequation>

In the field of global optimization many efforts have been devoted to solve unconstrained global optimization problems. The aim of this paper is to show that unconstrained global optimization methods can be used also for solving constrained optimization problems, by resorting to an exact penalty...

In this paper, we discuss the solution of linear and quadratic eigenvalue complementarity problems (EiCPs) using an enumerative algorithm of the type introduced by Júdice et al. (Optim. Methods Softw. 24:549–586, <CitationRef CitationID="CR1">2009</CitationRef>). Procedures for computing the interval that contains all the eigenvalues...</citationref>