INTRODUCTION Let F be a family of convex sets in R. A geometric transversal is an affine subspace that intersects every member of F . More specifically, for a given integer 0 ≤ k < d, a k-dimensional affine subspace that intersects every member of F is called a ktransversal to F . Typically, we are interested in necessary and sufficient conditions that guarantee the existence of a k-transversal...

This paper presents two meta-heuristic algorithms to solve an extended portfolio selection model. The extended model is based on the Markowitz's Model, aiming to minimize investment risk in a specified level of return. In order to get the Markowitz model close to the real conditions, different constraints were embedded on the model which resulted in a discrete and non-convex solution space. ...

The radial Dirac operator with a potential tending to infinity at infinity and satisfying a mild regularity condition is known to have a purely absolutely continuous spectrum covering the whole real line. Although having two singular end-points in the limit-point case, the operator has a simple spectrum and a generalised Fourier expansion in terms of a single solution. In the present paper, a s...

Convex relaxation methods have been studied and used extensively to obtain an optimal solution to the optimal power flow (OPF) problem. Meanwhile, convex relaxed power flow equations are also prerequisites for efficiently solving a wide range of problems in power systems including mixed-integer nonlinear programming (MINLP) and distributed optimization. When the exactness of convex relaxations ...

We derive a priori interior Hessian estimates for special Lagrangian equations when the potential is convex. When the phase is very large, we show that continuous viscosity solutions are smooth in the interior of the domain. c 2008 Wiley Periodicals, Inc.

Inspired by the penalization of the domain approach of Lions & Sznitman, we give a sense to Neumann and oblique derivatives boundary value problems for nonlocal, possibly degenerate elliptic equations. Two different cases are considered: (i) homogeneous Neumann boundary conditions in convex, possibly non-smooth and unbounded domains, and (ii) general oblique derivatives boundary conditions in s...

When a hypersurface (t) evolves with normal velocity equal to its mean curvature plus a forcing term g(x; t); the generalized (viscosity) solution may be \fattened" at some moment when (t) is singular. This phenomenon corresponds to nonuniqueness of codimension-one solutions. A speciic type of geometric singularity occurs if (t) includes two smooth pieces, at the moment t = 0 when the two piece...

A deterministic infinite-horizon singular control problem with unbounded control set is solved completely. The methods used here are those of dynamic programming and viscosity solutions. The novelty is that the value function is convex, C along a piece of the free boundary and not C along another piece of it.

A learning algorithm for the estimation of the structure of nonlinear recurrent neural models from neural tuning data is presented. The proposed method combines support vector regression with additional constraints that result from a stability analysis of the dynamics of the )tted network model. The optimal solution can be determined from a single convex optimization problem that can be solved ...

A unified methodology is presented for solving general global optimization problems. Based on the canonical dualitytriality theory, the nonconvex/nonsmooth/discrete problems from totally different systems are reformulated as a canonical min–max problem, which is equivalent to a monotone variational inequality problem over a convex cone. Therefore, a complementary-dual projection method is used ...