We present some sufficient conditions ensuring the upper semicontinuity and the continuity of the Bregman projection operator Π g C and the relative projection operator P g C in terms of the D-approximate (weak) compactness for a nonempty closed set C in a Banach space X . We next present certain sufficient conditions as well as equivalent conditions for the convexity of a Chebyshev subset of a...

We use a concept of abstract convexity to define the almost S-KKM C property, al-S-KKM C X, Y family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors. Copyright q 2009 Tong-Huei Chang et al. This is an open access article distributed under the Creative Commons Attribution License,...

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal newton algorithm with multi-stage convex relaxation based on the difference of convex (DC) programming, and enjoys both strong computational and statistical guarantees. Specifically, by leveraging a sophisticated characterization...

The land-acquisition problem involves selecting multiple discrete parcels to be acquired for a particular land use. In previous models, typical selection criteria have been land cost, land area, and spatial attributes such as contiguity and compactness. Here I introduce a new spatial attribute, convexity. I develop a way to approximate convex shapes in continuous space with `cellularly convex' ...

In the following proofs, we approximate demand and control variables as continuous when we prove the convexity of cost functions. In addition, unless otherwise noted, we use (f(x))′ to denote the derivative with respect to x and (g(x, y))′ to denote the partial derivative with respect to the first argument x for any continuous and differentiable functions f(x) and g(x, y). Finally, we need the ...

In order to better approximate and understand the exchange-correlation functional in density functional theory, the adiabatic connection curve is accurately calculated beyond the physical interaction strength using a simulated scaling method. This is done for Hooke’s atom, two interacting electrons in a harmonic well potential. Extrapolation of the accurate curve to the infinite-coupling limit ...

in this paper, we study the convexity of the integral operator

The game-theoretic analysis of Energy Efficiency (EE) game is known to be difficult due the non-convexity EE-utility, especially for tracing Nash Equilibrium in MIMO system. In this paper, existence and uniqueness (NE) affirmed a multiple access channel (MAC) communication system bisection search algorithm designed find unique NE. Despite being sub-optimal deploying approximate best response, p...

Abstract We design and analyze a $$C^0$$ C 0 interior penalty method for the approximation of classical solutions Dirichlet boundary value problem Monge–Ampère equation on convex polygonal domains. The is based an enhanced cubic Lagrange finite element that enables enfo...