In this paper we study relations between the directional derivatives, the weak subdifferentials, and the radial epiderivatives for nonconvex real-valued functions. We generalize the well-known theorem that represents the directional derivative of a convex function as a pointwise maximum of its subgradients for the nonconvex case. Using the notion of the weak subgradient, we establish conditions...

Radial axes plots are multivariate visualization techniques that extend scatterplots in order to represent high-dimensional data as points on an observable display. Well-known methods include star coordinates or principal component biplots, which represent data attributes as vectors that define axes, and produce linear dimensionality reduction mappings. In this paper we propose a hybrid approac...

We propose an alternative method for computing e¤ectively the solution of the control inventory problem under non-convex polynomial cost functions. We apply the method of moments in global optimization to transform the corresponding, non-convex dynamic programming problem into an equivalent optimal control problem with linear and convex structure. We device computational tools based on convex o...

We take a new approach to investigate synchronization in networks of coupled oscillators. We show that the coupled oscillator system when restricted to a proper region is a distributed partial primal-dual gradient algorithm for solving a well-defined convex optimization problem and its dual. We characterize conditions for synchronization solution of the KKT system of the optimization problem, b...

Consider the energy critical focusing wave equation on the Euclidian space. A blow-up type II solution of this equation is a solution which has finite time of existence but stays bounded in the energy space. The aim of this work is to exhibit universal properties of such solutions. Let W be the unique radial positive stationary solution of the equation. Our main result is that in dimension 3, u...

a compact formulation of the set of tours neither in a graph nor its complement is presented and illustrates a general methodology proposed for constructing polyhedral models of decision problems based upon permutations, projection and lifting techniques. directed hamilton tours on n vertex graphs are interpreted as (n-1)- permutations. sets of extrema of birkhoff polyhedra are mapped to tours ...

This paper undertakes the problem of optimal shunt capacitor placement for loss reduction in a radial distribution feeder. The objective is to determine the optimum size and location of the capacitors to be placed on a radial distribution system. The objective function is to have maximization of saving due to reduction of energy losses thereby taking into consideration cost of capacitor. The so...

The problem Minimum Convex Cover of covering a given polygon with a minimum number of (possibly overlapping) convex polygons is known to be NP -hard, even for polygons without holes [3]. We propose a polynomial-time approximation algorithm for this problem for polygons with or without holes that achieves an approximation ratio of O(logn), where n is the number of vertices in the input polygon. ...

In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...

An analytical solution is presented that reconstructs residual stress field from limited and incomplete data.  The inverse problem of reconstructing residual stresses is solved using an appropriate form of the airy stress function.  This function is chosen to satisfy the stress equilibrium equations together with the boundary conditions for a domain within a convex polygon.  The analytical solu...