We present some basic properties and equivalent definitions of the p-quasiconvex hull of a given set of matrices. In particular, we completely characterize the p-quasiconvex hull in terms of the W -gradient Young measures studied by [9] and establish an important relationship with the weak convergence in Sobolev spaces. We also give some simple characterization of the p-quasiconvex hulls for ce...

In this paper, we generalize the extended supporting hyperplane algorithm for a convex continuously differentiable mixed-integer nonlinear programming problem to solve a wider class of nonsmooth problems. The generalization is made by using the subgradients of the Clarke subdifferential instead of gradients. Consequently, all the functions in the problems are assumed to be locally Lipschitz con...

This paper extends the full convergence of the proximal point method with Riemannian, Semi-Bregman and Bregman distances to solve minimization problems on Hadamard manifolds. For the unconstrained problem, under the assumptions that the optimal set is nonempty and the objective function is continuous and either quasiconvex or satisfies a generalized Lojasiewicz property, we prove the full conve...

A group is called coherent when all of its finitely generated subgroups are finitely presented. Although many examples of coherent groups are known, (most notably polycyclic groups and 3-manifold groups) few tests are known for positively determining the coherence of an arbitrary group presentation. In this article we provide such a test. The test is based upon a definition of the perimeter of ...