We propose new techniques for the solution of the LP relaxation and the Lagrangean dual in combinatorial optimization problems. Our techniques find the optimal solution value and the optimal dual multipliers of the LP relaxation and the Lagrangean dual in polynomial time using as a subroutine either the Ellipsoid algorithm or the recent algorithm of Vaidya. Moreover, in problems of a certain st...

Abstract—Off-axis ellipsoid reflector based off-focus configuration for deastigmatism and circularization of an elliptical Gaussian beam is proposed. Mostly used off-axis ellipsoid reflector based conventional configuration is constructed by aligning the incident direction directed to one focus of the ellipsoid, which reflect the output beam to the another focus of the ellipsoid. However, such ...

We report current work on methods for robust fitting of ellipsoids to the shape of the human head in three-dimensional models built from laser scanner acquisitions. A starting ellipsoid is obtained from Principal Component Analysis from mesh vertices; those regions far from the surface of the ellipsoid are penalized (outlier rejection and/or damping). A first method consists in re-calculating i...

The problem of downward continuation of the gravity field from the Earth’s surface to the reference ellipsoid arises from the fact that the solution to the boundary value problem for geoid determination without applying Stokes formula is sought in terms of the disturbing potential on the ellipsoid but the gravity observations are only available on the Earth’s surface. Downward continuation is a...

In this paper we examine the problem of reconstructing a (possibly dynamic) ellipsoid from its (possibly inconsistent) orthogonal silhouette projections. We present a particularly convenient representation of ellipsoids as elements of the vector space of symmetric matrices. The relationship between an ellipsoid and its orthogonal projections in this representation is linear, unlike the standard...

Independent Component Analysis (ICA) is the problem of learning a square matrix A, given samples of X = AS, where S is a random vector with independent coordinates. Most existing algorithms are provably efficient only when each Si has finite and moderately valued fourth moment. However, there are practical applications where this assumption need not be true, such as speech and finance. Algorith...

We propose techniques for the solution of the LP relaxation and the Lagrangean dual in combinatorial optimization and nonlinear programming problems. Our techniques find the optimal solution value and the optimal dual multipliers of the LP relaxation and the Lagrangean dual in polynomial time using as a subroutine either the Ellipsoid algorithm or the recent algorithm of Vaidya. Moreover, in pr...

In August 1993, heavy meteor activity caused the Olympus telecommunications satellite (S/C) to lose Earth pointing attitude. Automatic emergency reacquisition maneuvers consumed so much propellant that the mission had to be terminated one year ahead of schedule. This paper reexamines the Olympus scenario using a recently proposed adaptive control scheme. The proposed method is a \query-based" a...

This paper studies the problem of target control and how a virtual ellipsoid can avoid static obstacle. During motion to set, achieve under collision avoidance by keeping distance between We present solutions this in class closed-loop (feedback) controls based on Hamilton–Jacobi–Bellman (HJB) equation. Simulation results verify validity effectiveness our algorithm.