We consider the problem of minimizing an indefinite quadratic function over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions (d.c.) problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective stationary points and minima. We the...

We propose a new method for mathematical programs with complementarity constraints that is globally convergent to B-stationary points. The method solves a linear program with complementarity constraints to obtain an estimate of the active set. It then fixes the activities and solves an equality-constrained quadratic program to obtain fast convergence. The method uses a filter to promote global ...

Sample average approximation (SAA) method which is also known under various names such as Monte Carlo method, sample path optimization and stochastic counterpart has recently been applied to solve stochastic programs with second order stochastic dominance (SSD) constraints. In particular, Hu et al [19] presented a detailed convergence analysis of ε-optimal values and optimal solutions of sample...

In this manuscript, density functional theory was used to explore structural, vibrational and optical properties of the (Sc2O3)n (n=1-5) cluster systems using DFT/B3LYP/LanL2DZ level of computation. Different stable isomers were obtained and numerous chemical parameters such as HOMO-LUMO gap, ionization potential and electron affinity were calculated successfully. Stability of the clusters was ...

The mean shift (MS) algorithm is a non-parametric, iterative technique that has been used to find modes of an estimated probability density function (pdf). Although the MS algorithm has been widely used in many applications, such as clustering, image segmentation, and object tracking, a rigorous proof for its convergence is still missing. This paper tries to fill some of the gaps between theory...

Conditional Value at Risk (CVaR) has been recently used to approximate a chance constraint. In this paper, we study the convergence of stationary points when sample average approximation (SAA) method is applied to a CVaR approximated joint chance constrained stochastic minimization problem. Specifically, we prove, under some moderate conditions, that optimal solutions and stationary points obta...

We present a novel variation of the well-known infomax algorithm of blind source separation. Under natural gradient descent, the infomax algorithm converges to a stationary point of a limiting ordinary differential equation. However, due to the presence of saddle points or local minima of the corresponding likelihood function, the algorithm may be trapped around these “bad” stationary points fo...

The governing equation is ut= a x ux x, 0 x 1, t 0, u x ,0 =0, u 0, t =0, a 1 u 1, t = f t . The extra data are u 1, t =g t . It is assumed that a x is a piecewise-constant function and f 0. It is proved that the function a x is uniquely defined by the above data. No restrictions on the number of discontinuity points of a x and on their locations are made. The number of discontinuity points is ...

Subdivision is a convenient tool to construct objective curves and surfaces directly from given scattered points. Stationary p-subdivision schemes are highly efficient in the acquisitions of curve/surface points in shape modeling. The features of supported set of nonnegative mask of uniform convergent stationary subdivision schemes are important to their theoretic researches and applications. A...

If G is a transformation group on a space X, then x(~X is a stationary point if gx = x for every g £ G . It has been an open problem, proposed by Smith [5] and by Montgomery [l, Problem 39], to determine whether every compact Lie group acting on a cell or on Euclidean space has a stationary point. Smith [4; 5] has shown the answer to be in the affirmative in case G is a toral group or a finite ...