The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space. We introduce implicit and explicit iterative algorithms which converge strongly to a unique solution of the hierarchical variational inequality problem. Our results improve and extend the corr...

An explicit hierarchical fixed point algorithm is introduced to solve the monotone variational inequality over the fixed point set of a nonexpansive mapping. This paper discusses a monotone variational inequality with variational constraint and convex optimization problems over the fixed point set of a nonexpansive mapping. The strong convergence for the proposed algorithm to the solution is gu...

In this paper, we examine the duality gap between the robust counterpart of a primal uncertain convex optimization problem and the optimistic counterpart of its uncertain Lagrangian dual and identify the classes of uncertain problems which do not have a duality gap. The absence of a duality gap (or equivalently zero duality gap) means that the primal worst value equals the dual best value. We f...

We study an equivalent optimization problem with an inequality constraint and boundary conditions, whose necessary condition for the optimality is the variational inequality presentation of American options. To solve the problem, we use the gradient projection method, with discretizations both in time and space. We tested the algorithm and compared with the projective successive over-relaxation...

Redundant constraints in linear inequality systems can be characterized as those inequalities that can be removed from an arbitrary linear optimization problem posed on its solution set without modifying its value and its optimal set. A constraint is saturated in a given linear optimization problem when it is binding at the optimal set. Saturation is a property related with the preservation of ...

We consider semidefinite optimization problems that include constraints of the form G(x) 0 and H(x) 0, where the components of the symmetric matrices G(·) and H(·) are affine functions of x ∈ Rn. In such a case we obtain a new constraint K(x,X) 0, where the components of K(·, ·) are affine functions of x and X, and X is an n×n matrix that is a relaxation of xxT . The constraint K(x,X) 0 is base...

Generalized Nash games represent an extension of Nash games in which strategy sets are coupled across players. The equilibrium conditions of such a game can be compactly stated as a quasivariational inequality (QVI), an extension of the variational inequality (VI). Harker [9] showed that under certain conditions on the maps defining the QVI, a solution to a related VI solves the QVI. This is a ...

We prove that the log-determinant of the covariance matrix obeys the strong subadditivity inequality for arbitrary tripartite states of multimode continuous variable quantum systems. This establishes general limitations on the distribution of information encoded in the second moments of canonically conjugate operators. The inequality is shown to be stronger than the conventional strong subaddit...

A maximum entropy (ME) model is usually estimated so that it conforms to equality constraints on feature expectations. However, the equality constraint is inappropriate for sparse and therefore unreliable features. This study explores an ME model with box-type inequality constraints, where the equality can be violated to reflect this unreliability. We evaluate the inequality ME model using text...