Given a function on Rn with many multiple local minima we approximate it from below, via concave minimization, with a piecewise-linear convex function by using sample points from the given function. The piecewise-linear function is then minimized using a single linear program to obtain an approximation to the global minimum of the original function. Successive shrinking of the original search r...

This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality f(x; y; z) 0. The volume spline is based on use of the Green's function for interpolation of scalar function values of a chosen "carrier" solid. Our algorithm is capable of generating highly conc...

The goal of this paper is to introduce the notion of certificates, which verify the accuracy of solutions of computational problems with convex structure. Such problems include minimizing convex functions, variational inequalities with monotone operators, computing saddle points of convex-concave functions, and solving convex Nash equilibrium problems. We demonstrate how the implementation of t...

This paper presents a novel approach to the reconstruction of geometric models and surfaces from given sets of points using volume splines. It results in the representation of a solid by the inequality The volume spline is based on use of the Green’s function for interpolation of scalar function values of a chosen “carrier” solid. Our algorithm is capable of generating highly concave and branch...

We consider stochastic programming problems with probabilistic constraints in volving integer valued random variables The concept of p e cient points of a prob ability distribution is used to derive various equivalent problem formulations Next we modify the concept of r concave discrete probability distributions and analyse its relevance for problems under consideration These notions are used t...

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar (1987). The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen, Samworth and...

In curve design such as highway design andmotion planning of autonomous vehicles, it may be important to minimize the maximum curvature. In this paper we address the problem of minimizing the maximum curvature of a quadratic Bézier curve within a boundary constraint determined by a tetragonal concave polygon. The curve is parameterized by lengths between its control points, called the ‘‘control...

Poor convergence to concave boundaries is a limitation in the use of snakes as a contour approximation technique. The external force for active contours, called gradient vector flow (GVF), has provided a remarkable improvement to this problem. However, the technique requires high computation time for reliable concavity performance. In this paper, we propose an efficient solution to overcome the...

The paper describes an optimal design of poly-phase filter for up-sampling of audio signals. The design of filter is based on Teaching-Learning-Based Optimization (TLBO) algorithm. To obtain a digital filter that maintains the sequence of original signal points and at the same time increase the sampling rate with no change in shape of its spectrum, TLBO algorithm is applied and results are illu...

This paper presents a decomposition scheme for a large class of greyscale structuring elements from mathematical morphology. In contrast with many existing decomposition schemes, our method is valid in the continuous domain. Conditions are given under which this continuous method can be properly discretized. The class of functions that can be decomposed with our method contains the class of qua...