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
We extend recent work on mixed-integer nonlinear optimal control prob- lems (MIOCPs) to the case of integer control functions subject to constraints. Promi- nent examples of such systems include problems with restrictions on the number of switches permitted, or problems that minimize switch cost. We extend a theorem due to [Sager et al., Math. Prog. … Read more
We study local convergence of generalized Newton methods for both equations and inclusions by using known and new approximations and regularity properties at the solution. Including Kantorovich-type settings, our goal are statements about all (not only some) Newton sequences with appropriate initial points. Our basic tools are results of Klatte-Kummer (2002) and Kummer (1988, 1995), … Read more
An approach for solving quasi-equilibrium problems (QEPs) is proposed relying on gap functions, which allow reformulating QEPs as global optimization problems. The (generalized) smoothness properties of a gap function are analysed and an upper estimates of its Clarke directional derivative is given. Monotonicity assumptions on both the equilibrium and constraining bifunctions are a key tool … Read more
Let K be a closed convex cone with dual K^* in a finite-dimensional real inner-product space V. The complementarity set of K is C(K) = { (x, s) in K × K^* | = 0 }. We say that a linear transformation L : V -> V is Lyapunov-like on K if = 0 for all (x, … Read more
In this paper, we present a new computation scheme for pessimistic bilevel optimization problem, which so far does not have any computational methods generally applicable yet. We first develop a tight relaxation and then design a simple scheme to ensure a feasible and optimal solution. Then, we discuss using this scheme to compute linear pessimistic … Read more
In this paper, we introduce a new explicit iterative algorithm for finding a solution of split variational inclusion problem over the common fixed points set of a infinite family of nonexpansive mappings in Hilbert spaces. To reach this goal, the iterative algorithms which combine Tian’s method with some fixed point technically proving methods are utilized … Read more
In this paper we consider a mathematical program with second-order cone complementarity constraints (SOCMPCC). The SOCMPCC generalizes the mathematical program with complementarity constraints (MPCC) in replacing the set of nonnegative reals by a second-order cone. We show that if the SOCMPCC is considered as an optimization problem with convex cone constraints, then Robinson’s constraint qualification … Read more
This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a constant stepsize. It is similar to the projected gradient method, namely, the method requires only one projection onto the feasible set and only … Read more
It is known that the complementarity problems and the variational inequality problems are reformulated equivalently as a vector equation by using the natural residual or Fischer-Burmeister function. In this short paper, we first study the global convergence of a sequential injective algorithm for weakly univalent vector equation. Then, we apply the convergence analysis to the … Read more