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 a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\alpha $$</EquationSource> </InlineEquation> <Emphasis Type="SmallCaps">BB method and convergence to global minimizers was obtained assuming feasibility of the...</emphasis></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...

The nonlinear convex programming problem of finding the minimum covering weighted ball of a given finite set of points in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\mathbb{R}^n}$$</EquationSource> </InlineEquation> is solved by generating a finite sequence of subsets of the points and by finding the minimum covering weighted ball of each subset in the sequence until...</equationsource></inlineequation>

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 nonlinear programming problems, we propose a new class of smooth exact penalty functions, which includes both barrier-type and exterior-type penalty functions as special cases. We develop necessary and sufficient conditions for exact penalty property and inverse proposition of exact...

We study a game model of multi-leader and one-follower in supply chain optimization where n suppliers compete to provide a single product for a manufacturer. We regard the selling price of each supplier as a pre-determined parameter and consider the case that suppliers compete on the basis of...

Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality...

This paper presents a new nonlinear programming problem arising in the control of power systems, called optimal power flow with transient stability constraint and variable clearing time of faults and abbreviated as OTS-VT. The OTS-VT model is converted into a implicit generalized semi-infinite...