Related papers: Extended Lorentz cones and variational inequalitie…
Differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides in R^n are studied. Under a weakened monotonicity-type condition the existence of solutions is proved.
By using the metric projection onto a closed self-dual cone of the Euclidean space, M. S. Gowda, R. Sznajder and J. Tao have defined generalized lattice operations, which in the particular case of the nonnegative orthant of a Cartesian…
For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic…
We consider the variational inequality problem over the intersection of fixed point sets of firmly nonexpansive operators. In order to solve the problem, we present an algorithm and subsequently show the strong convergence of the generated…
We consider the Frank-Wolfe algorithm for solving variational inequalities over compact, convex sets under a monotone $C^1$ operator and vanishing, nonsummable step sizes. We introduce a continuous-time interpolation of the discrete…
We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a…
Proper cones with the property that the projection onto them is isotone with respect to the order they induce are called isotone projection cones. Isotone projection cones and their extensions have been used to solve complementarity…
If Lorentz symmetry is broken, it must have occurred dynamically, via a vector or tensor field whose potential energy forces it to take on a non-zero background expectation value "in vacuum". If the set of minima of this potential (the…
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
We derive a closed-form expression for the projection onto a capped rotated second-order cone -- a convex set that arises in perspective relaxations of nonlinear programs with binary indicator variables. The closed-form solution involves…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…
A large number matrix optimization problems are described by orthogonally invariant norms. This paper is devoted to the study of variational analysis of the orthogonally invariant norm cone of symmetric matrices. For a general orthogonally…
Moment inequality for quadratic forms of random vectors is of particular interest in covariance matrix testing and estimation problems. In this paper, we prove a Rosenthal-type inequality, which exhibits new features and certain improvement…
We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no condition on the boundary of the cone. We show the…
A wedge (i.e., a closed nonempty set in the Euclidean space stable under addition and multiplication with non-negative scalars) induces by a standard way a semi-order (a reflexive and transitive binary relation) in the space. The wedges…
The property of isotonicity of a continuous convex function defined on the entire space or only on the positive cone is characterized via subdifferentials. Numerous examples illustrating the obtained results are included.
Suppose given a commutative quadrangle in a Verdier triangulated category such that there exists an induced isomorphism on the horizontally taken cones. Suppose that the endomorphism ring of the initial or the terminal corner object of this…