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 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>

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...

Effective risk management requires adequate risk measurement. A basic problem herein is the quantification of market risks: what is the overall effect on a portfolio if market rates change? First, a mathematical problem statement is given and the concept of `Maximum Loss' (ML) is introduced as a...

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...

Effective risk management requires adequate risk measurement. A basic problem herein is the quantification of market risks: what is the overall effect on a portfolio if market rates change? First, a mathematical problem statement is given and the concept of `Maximum Loss' (ML) is introduced as a...

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...

For univariate functions, we compute optimal breakpoint systems subject to the condition that the piecewise linear approximation (or, under- and overestimator) never deviates more than a given δ-tolerance from the original function, over a given finite interval. The linear approximators, under-...