We establish an isoperimetric inequality with constraint by ndimensional lattices. We prove that, among all domains which consist of rectangular parallelepipeds with the common side-lengths, a cube is the best shape to minimize the ratio involving its perimeter and volume as long as the cube is realizable by the lattice. For its proof a solvability of finite difference PoissonNeumann problems i...

This paper presents novel results about the structure of solutions for certain evolutionary variational inequality problems. We show that existence of piecewise solutions is dependant upon the form of the constraint set underlying the evolutionary variational inequality problem considered. We discuss our results in the context of double-layered dynamics theory and we apply them to the modelling...

Abstract. There is a family of potentials that minimize the lowest eigenvalue of a Schrödinger eigenvalue under the constraint of a given L norm of the potential. We give effective estimates for the amount by which the eigenvalue increases when the potential is not one of these optimal potentials. Our results are analogous to those for the isoperimetric problem and the Sobolev inequality. We al...

Characterizations of global optimality are given for general difference convex (DC) optimization problems involving convex inequality constraints. These results are obtained in terms of E-subdifferentials of the objective and constraint functions and do not require any regularity condition. An extension of Farkas’ lemma is obtained for inequality systems involving convex functions and is used t...

A class of discrete convex functions that can efficiently be minimized has been considered by Murota. Among them are L\-convex functions, which are natural extensions of submodular set functions. We first consider the problem of minimizing an L\-convex function with a linear inequality constraint having a positive normal vector. We propose a polynomial algorithm to solve it based on a binary se...

It has long been known that variational inequality problems can be reformulated as nonsmooth equations. Recently, locally high-order convergent Newton methods for nonsmooth equations have been well established via the concept of semismoothness. When the constraint set of the variational inequality problem is a rectangle, several locally convergent Newton methods for the reformulated nonsmooth e...

Structural vibration mitigation using semiactive control strategies has received special attention recently due to the attractive properties of semiactive devices. The main restriction of a semiactive device is that it can only produce dissipative forces, which may be expressed in mathematical terms as a nonlinear inequality constraint. Standard active control algorithms do not generally accoun...

In this paper, we consider minimization problems with a quasiconvex vector-valued inequality constraint. We propose two constraint qualifications, the closed cone constraint qualification for vector-valued quasiconvex programming (the VQ-CCCQ) and the basic constraint qualification for vector-valued quasiconvex programming (the VQ-BCQ). Based on previous results by Benoist, Borwein, and Popovic...

We describe an infeasible-interior-pointalgorithmfor monotone variational inequality problems and prove that it converges globally and superlinearly under standard conditions plus a constant rank constraint quali cation. The latter condition represents a relaxation of the two types of assumptions made in existing superlinear analyses; namely, linearity of the constraints and linear independence...

We develop an active set method for solving second-order cone programs that may have an arbitrary number of linear constraints but are restricted to have only one second-order cone constraint. Problems of this form arise in the context of robust optimization and trust region methods. The proposed active set method exploits the fact that a second-order cone program with only one second-order con...