Lyapunov rank of polyhedral positive operators

If K is a closed convex cone and if L is a linear operator having L(K) a subset of K, then L is a positive operator on K and L preserves inequality with respect to K. The set of all positive operators on K is denoted by pi(K). If J is the dual of K, … Read more

Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities

A model for Nash-Cournot oligopolistic markets with concave cost functions and a differentiated commodity is analysed. Equilibrium states are characterized through Ky Fan inequalities. Relying on the minimization of a suitable merit function, a general algorithmic scheme for solving them is provided. Two concrete algorithms are therefore designed that converge under suitable convexity and monotonicity … Read more

A Penalty Method for Rank Minimization Problems in Symmetric Matrices

The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. We investigate calmness of locally optimal solutions to the SDCMPCC formulation and hence show that any locally optimal … Read more

Computing Feasible Points for Binary MINLPs with MPECs

Nonconvex mixed-binary nonlinear optimization problems frequently appear in practice and are typically extremely hard to solve. In this paper we discuss a class of primal heuristics that are based on a reformulation of the problem as a mathematical program with equilibrium constraints. We then use different regularization schemes for this class of problems and use … Read more

How to project onto extended second order cones

The extended second order cones were introduced by S. Z. Németh and G. Zhang in [S. Z. Németh and G. Zhang. Extended Lorentz cones and variational inequalities on cylinders. J. Optim. Theory Appl., 168(3):756-768, 2016] for solving mixed complementarity problems and variational inequalities on cylinders. R. Sznajder in [R. Sznajder. The Lyapunov rank of extended … Read more

Solving Linear Programs with Complementarity Constraints using Branch-and-Cut

A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a modeling paradigm for a broad collection of problems, including bilevel programs, Stackelberg games, inverse quadratic programs, and problems involving equilibrium constraints. The … Read more

Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take … Read more

A Study of the Difference-of-Convex Approach for Solving Linear Programs with Complementarity Constraints

This paper studies the difference-of-convex (DC) penalty formulations and the associated difference-of-convex algorithm (DCA) for computing stationary solutions of linear programs with complementarity constraints (LPCCs). We focus on three such formulations and establish connections between their stationary solutions and those of the LPCC. Improvements of the DCA are proposed to remedy some drawbacks in a … Read more

Evaluating the effect of environmental regulations on a closed-loop supply chain network: a variational inequality approach

Global climate change has encouraged international and regional adoption of pollution taxes and carbon emission reduction policies. Europe has taken the leadership in environmental regulations by introducing the European Union Emissions Trading System (EU-ETS) in 2005 and by developing and promoting a set of policies destined to lower carbon emissions from transport sectors. These environmental … Read more

Decomposition Method for Oligopolistic Competitive Models with Common Pollution Regulation

We consider the general problem of industrial production in a set of countries subject to a common environmental regulation that limits the emissions of specific sectors. Due to these restrictions, the problem is treated as a generalized non-cooperative game where players (countries) have joint (environmental) constraints caused by the necessity of a common and compulsory … Read more