In this work we study the existence of nontrivial solution for the following class of multivalued quasilinear problems <Equation ID="Equ51"> <EquationSource Format="TEX">$$\begin{aligned} \displaystyle -\text{ div } ( \phi (|\nabla u|) \nabla u) - b(u)u \in \lambda \partial F(x,u)\;\text{ in }\;\Omega , \quad u=0\; \text{ on }\;\partial \Omega...</equationsource></equation>

In this paper, we propose interior-point algorithms for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$P_* (\kappa )$$</EquationSource> </InlineEquation>-linear complementarity problem based on a new class of kernel functions. New search directions and proximity measures are defined based on these functions. We show that if a strictly feasible starting point is available,...</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 this paper we consider two branch and bound algorithms for the maximum clique problem which demonstrate the best performance on DIMACS instances among the existing methods. These algorithms are MCS algorithm by Tomita et al. (<CitationRef CitationID="CR31">2010</CitationRef>) and MAXSAT algorithm by Li and Quan (<CitationRef CitationID="CR21">2010a</CitationRef>, <CitationRef CitationID="CR22">b</CitationRef>). We suggest a...</citationref></citationref></citationref>

This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations...

We propose an entire space polynomial-time algorithm for linear programming. First, we give a class of penalty functions on entire space for linear programming by which the dual of a linear program of standard form can be converted into an unconstrained optimization problem. The relevant...

We study a general equilibrium model formulated as a smooth system of equations coupled with complementarity conditions relative to the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$n$$</EquationSource> </InlineEquation>-dimensional Lorentz cone. For the purpose of analysis, as well as for the design of algorithms, we exploit the fact that the Lorentz cone is...</equationsource></inlineequation>

Given a point on the standard simplex, we calculate a proximal point on the regular grid which is closest with respect to any norm in a large class, including all <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\ell ^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math> </EquationSource> </InlineEquation>-norms for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$p\ge 1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>p</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math> </EquationSource> </InlineEquation>. We show that the minimal <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\ell ^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math> </EquationSource> </InlineEquation>-distance to the...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The well-known Shortest Path problem (SP) consists in finding a shortest path from a source to a destination such that the total cost is minimized. The SP models practical and theoretical problems. However, several shortest path applications rely on uncertain data. The Robust Shortest Path...

The paper studies a nonlinear optimization problem under resource allocation constraints. Using quasi-gradient duality it is shown that the feasible set of the problem is a singleton (in the case of a single resource) or the set of Pareto efficient solutions of an associated vector maximization...