Where results make sense

About us   |   Why use us?   |   Reviews   |   PR   |   Contact us

Topic: Ellipsoid method

    Note: these results are not from the primary (high quality) database.

IITBHF and IITBAA (http://www.iitbombay.org) Consequently, the ellipsoid method is faster than the simplex method in contrived cases where the simplex method performs poorly. In 1979, Leonid Khaciyan presented the ellipsoid method, guaranteed to solve any linear program in a number of steps which is a polynomial function of the amount of data defining the linear program. In brief, the simplex method passes from vertex to vertex on the boundary of the feasible polyhedron, repeatedly increasing the objective function until either an optimal solution is found, or it is established that no solution exists. www.iitbombay.org /misc/press/karmarkar.htm

Very Deep Cuts and two Cuts in the Analytic Center Cutting Plane Method If the oracle generates a cut that goes beyond the Dikin ellipsoid, the cutting plane is shifted backward, a procedure that is liable to slow down the method in practice. The standard method assumes that a new cut either passes through the analytic center, or intersects the Dikin ellipsoid. We propose two extensions of the basic analytic center cutting plane method, and provide complexity estimates for the two cases. roso.epfl.ch /ismp97/ismp_abs_1180.html

Articles - Linear programming It was based on the ellipsoid method in nonlinear optimization by Naum Shor, which is the generalization of the ellipsoid method in convex optimization by Arkadi Nemirovski, a 2003 John von Neumann Theory Prize winner, and D. Yudin. A popular interior point method is the Mehrotra predictor-corrector method, which performs very well in practice even though little is known about it theoretically. This method is also classified as NP-hard, and in fact the decision version was one of Karp's 21 NP-complete problems. www.kamero.net /articles/Linear_programming

GeodeticsComponents10.doc A second method of referencing the ellipsoid is by using the object reference. The parameters of the ellipsoid and the prime meridian are useful to transformations, are are carried along with the datum definition. SemiMajorAxis: The length of the semimajor axis of the ellipsoid of revolution. www.posc.org /ComponentDocs/GeodeticsComponents10.doc   (6365 words)

Ellipsoid Method If, however, the ellipsoid method terminates without finding a point in Q, Q may be empty or may be non-empty and not full-dimensional. So, to solve (1), we can apply the ellipsoid method to the set Q defined in (2). , we may perform the ellipsoid method on the polytope P www.ms.uky.edu /~sills/webprelim/chap13.html   (623 words)

Re: Geo::Ellipsoid module > she didn't get the ellipsoid specified, just to guard against typos. I would probably have had a separate method to change the > > $e2 will have an ellipsoid 'IAU76'. www.1-script.com /forums/Re-GeoEllipsoid-module-article3452-5.htm   (215 words)

karmarkar > >Yes, but the ellipsoid method was only of theoretical interest >and not very practical. Interior point methods were a scientific revolution that couldn't happen until all of the bits and pieces were available and until a new generation of researchers came along who were trained in the required areas of computer science (analysis of algorithms, computational complexity, etc.), numerical linear algebra, and optimization. The fastest method for a particular problem depends on the details of the problem, the details of the implementations of the simplex and interior point methods used, as well as the computer that is being used. www.math.niu.edu /~rusin/known-math/01_incoming/karmarkar   (1332 words)

Archimedes's method It provides a glimpse into the thinking which led Archimedes to many of his famous results, including the determination of the area of a parabola, the area and volume of a sphere, and the volume of an ellipsoid. From The Method of Archimedes (the translation is that of T.L. Heath): The Method proved a revolution in the understanding of Archimedes’ thought. www.cut-the-knot.org /pythagoras/Archimedes.shtml   (747 words)

SCO Web: Wisconsin County Coordinate Systems Since the Wisconsin systems were designed using the parallel ellipsoid method, a new reference ellipsoid needs to be defined for each local system by adding the value in Wisconsin) to the semi-major and semi-minor axes of the GRS 80 ellipsoid used to define the NAD 83 datum. As mentioned earlier, each county coordinate system was developed by introducing a local parallel ellipsoid that passes through the median elevation of the area. The purpose of the Wisconsin County Coordinate System is to provide a mathematically rigorous and more convenient method for relating ground measurement to geodetic control and other coordinate values. www.geography.wisc.edu /sco/pubs/wiscoord/county.php   (747 words)

The Mathematical Tourist Like the ellipsoid method, Narendra Karmarkar's scheme also runs in polynomial time, but the exponent governing how long his method takes is smaller than the exponent governing the ellipsoid method. Karmarkar's method pushes up the number of variables and constraints that can be handled within a reasonable time. In the last few years, a new, remarkably efficient method, discovered by Narendra K. Karmarkar of ATandT Bell Laboratories, has taken the spotlight. www.fortunecity.com /emachines/e11/86/tourist4e.html   (1791 words)

SMI - GPS The typical method of converting from ellipsoid positions to local coordinates is to flatten them using some standard projection method and then rotate, translate, and scale from the standard projection to the local coordinates. Local coordinates are in a plane, not an ellipsoid. One of the difficulties in using GPS in a local coordinate system is that the receiver provides ellipsoidal positions in latitude, longitude, and ellipsoidal height. www.smi.com /gps/Simple.htm   (1061 words)

24728.010412&ELEMENT_SET=DECL A method of ablating a cornea into a prolate shape in accordance with still another aspect of the present invention comprises determining a desired ablation pattern to form a prolate shaped ellipsoid on a surface of the cornea. An eccentricity of the prolate shaped ellipsoid is adjusted to intentionally leave approximately 10% astigmatism on an ablated surface of the cornea to cancel an astigmatic condition on a posterior side of the cornea and any contribution from lenticular astigmatism. Prolate ablation using ellipsoidal modeling with three (3) degrees of freedom in accordance with the principles of the present invention is best used with regular astigmatism. www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/24728.010412&ELEMENT_SET=DECL   (5199 words)

Science Fair Projects - Linear programming It was based on the ellipsoid method in nonlinear optimization by Naum Shor, which is the generalization of the ellipsoid method in convex optimization by Arkadi Nemirovski, a 2003 John von Neumann Theory Prize winner, and D. Yudin. However, the practical performance of Khachiyan's algorithm is disappointing: generally, the simplex method is more efficient. Its main importance is that it encouraged the research of interior point methods. www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Integer_program   (5199 words)

EPSG Guidance Note 7 For Conical map projections, which for the normal aspect may be considered as the projection of the ellipsoid onto an enveloping cone in contact with the ellipsoid along a parallel of latitude, the parallel of contact is known as a standard parallel and the scale is regarded as true along this parallel. For the stereographic projection the origin is at the centre of the projection where the plane of the map is imagined to be tangential to the ellipsoid. The projection's initial line may be selected as a line with a particular azimuth through a single point, normally at the centre of the mapped area, or as the geodesic line (the shortest line between two points on the ellipsoid) between two selected points. remotesensing.org /geotiff/proj_list/guid7.html   (8993 words)

More Information on Quasiconvex Optimizations and Location Theory (Applied Optimization, Vol. 9.) Discusses variants of the ellipsoid method for convex and quasiconvex problems and applies them to very general convex and quasiconvex models in location theory. This book includes variants of the ellipsoid method for convex and quasiconvex problems and applies them to very general convex and quasiconvex models in location theory. Although the techniques required by the quasiconvex case are more complex, the book provides a clear and direct interpretation of the main theoretical results. www.domsys.com /bookshop/p/Programming_Algorithms/Quasiconvex_Optimizations_and_Location_Theory_Applied_Optimization_Vol_9__0792346947.htm   (8993 words)

SIAM 2005 Optimization Conference Khachiyan and co-authors also developed polynomial-time algorithms for convex quadratic programming, studied the complexity of polynomial programming over the reals and the integers, and devised the method of inscribed ellipsoids for general convex programming. Khachiyan's analysis led to broad applications of the ellipsoid algorithm as a method of obtaining complexity results for discrete optimization problems. Khachiyan was best known for his 1979 use of the ellipsoid algorithm, originally developed for convex programming, to give the first polynomial-time algorithm to solve linear programming problems. www.siam.org /meetings/op05   (8993 words)

Mapping with GPS Data The purpose for state plane systems is to give surveyors a method for creating maps with minimal scale distortion that would be tied to a single national coordinate system. It uses the General Reference System of 1980 (GRS-80) ellipsoid which is nearly identical to the WGS84 ellipsoid. They include a reference ellipsoid, an ellipsoidal gravity equation, a terrestrial gravity model, a geoid and translations to other geodetic systems. ares.redsword.com /gps/old/sum_map.htm   (1731 words)

Mapping with GPS Data The purpose for state plane systems is to give surveyors a method for creating maps with minimal scale distortion that would be tied to a single national coordinate system. They include a reference ellipsoid, an ellipsoidal gravity equation, a terrestrial gravity model, a geoid and translations to other geodetic systems. It uses the General Reference System of 1980 (GRS-80) ellipsoid which is nearly identical to the WGS84 ellipsoid. ares.redsword.com /gps/old/sum_map.htm   (1731 words)

USIGS Definitions and Descriptions - G The quantities of latitude, longitude, and height (ellipsoid), which define the position of a point on the surface of the Earth with respect to the reference spheroid. A plane that contains the normal to the reference ellipsoid at a given point and the rotation axis of the reference ellipsoid. It is a method of expressing latitude and longitude in a form suitable for rapid reporting and plotting. www.fas.org /irp/agency/nima/nug/gloss_g.html   (1731 words)

World Geodetic System - Wikipedia, the free encyclopedia In accomplishing WGS 60, a combination of available surface gravity data, astro-geodetic data and results from HIRAN and Canadian SHORAN surveys were used to define a best-fitting ellipsoid and an earth-centered orientation for each of the initially selected datums (Chapter IV). The defining parameters of the WGS 66 Ellipsoid were the flattening (1/298.25), determined from satellite data and the semimajor axis (6,378,145 meters), determined from a combination of Doppler satellite and astro-geodetic data. Therefore, a motivation, and a substantial problem in the WGS and similar work is to patch together datums that were not only made separately, for different regions, but to re-reference the elevations to an ellipsoid model rather than to the geoid. en.wikipedia.org /wiki/WGS   (1839 words)

108-Li.htm The molecular dynamics method is used to simulate healing of an ellipsoid crack inside copper under compressive stress with EAM potential. The result shows that dislocations are emitted firstly from the ellipsoid crack and move along the 1\bar{1}1 and \bar{1}11 planes under a constant compressive stress of 0.34 GPa. The ellipsoid crack becomes smaller and smaller until it is healed through dislocation emission, motion, and annihilation on the surfaces. osiris.seas.ucla.edu /mmm/abstracts/s1/108-Li.htm   (147 words)

IITBHF and IITBAA (http://www.iitbombay.org) In 1984, Narendra Karmarkar introduced an interior-point method for linear programming, combining the desirable theoretical properties of the ellipsoid method and practical advantages of the simplex method. In 1984, Narendra Karmarkar (BTech EE '78) made a groundbreaking discovery in the field of Linear Programming while working at the famed Bell Labs in New Jersey. Narendra Karmarkar Citation For his theoretical work in devising an Interior Point www.iitbombay.org /misc/press/karmarkar.htm   (728 words)

ch11-4.htm Concerning techniques, the next major step in geodesy came when Tycho Brahe conceived of the method of triangulation, which was developed into a science by Willebrord Snell. This ellipsoid of revolution, with center at the origin of coordinates, was often used as reference ellipsoid before the advent of satellites. Physically the surfaces over which psi [Greek letter] is constant are the level surfaces discussed earlier in defining the geoid. www.hq.nasa.gov /office/pao/History/SP-4211/ch11-4.htm   (3380 words)

Pattern Classification Via Linear Programming It can be solved using the Simplex Method (Wood and Dantzig 1949), Interior Point Methods (Karmarkar 1984),and the Ellipsoid Method (Kachian 1979) among others. Linear Programming: The problem of maximizing (or minimizing) a linear function subject to a finite number of linear constraints, also known as Operations Research, Optimization Theory, or Convex Optimization Theory. In 1964 Mosteller and Wallace used statistical inference and came to the conclusion that Madison was the author of all 12 disputed papers. cgm.cs.mcgill.ca /~beezer/cs644/main.html   (1681 words)

IFS Competitive Examination Cartesian and polar coordinates in two and three dimensions, second degree equations in two and three dimensions, reduction to cannonical forms, straight lines, shortest distance between two skew lines, plane, sphere, cone, cylinder, paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties. Second order linear equations with, variable coefficients, determination of complete solution when one solution is known, method of variation of parameters. Numerical methods : Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods, solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct) methods, Gauss-Seidel (iterative) method. envfor.nic.in /legis/ifs/exam.html   (1681 words)

publ.html In the former case, the set of possible system states compatible with the observations received is shown to be an ellipsoid, and equations for its center and weighting matrix are given, while in the latter case, equations describing a bounding ellipsoid to the set of possible states are derived. This is the problem of finding a trajectory that starts at a given point, ends at the boundary of a compact set, and minimizes a cost function of the form $\int_0^Tr(x(t))dt+q(x(T)).$ For a discretized version of this problem, a Dijkstra-like method that requires one iteration per discretization point has been developed by Tsitsiklis. Bertsekas, L. Polymenakos, and P. Tseng, "Epsilon-Relaxation and Auction Methods for Separable Convex Cost Network Flow Problems," in Network Optimization, by P. Pardalos, D. Hearn, and W. Hager (eds.), Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, N.Y., 1998, pp. web.mit.edu /dimitrib/www/publ.html   (1681 words)

semidef.tex \end{example} \subsection{Algorithms for semidefinite programs I: the ellipsoid method} One can test if a symmetric matrix $A$ is positive semidefinite using the following algorithm: \smallskip \noindent {\bf Algorithm.} Carry out Gaussian elimination on $A$, pivoting always on diagonal entries. \end{corollary} \subsection{Algorithms for semidefinite programs II: interior point methods} Semidefinite programs can be solved in polynomial time and also {\it practically efficiently} by interior point methods \cite{Ov,Ali1,Ali2,NN1}. \section{Getting semidefinite programs I: spectra of graphs}\label{EIGEN} \subsection{Eigenvalue bounds and the method of variables} Let $G=(V,E)$ be a graph. www.cs.elte.hu /papers/semidef.tex   (1681 words)

CoordinateTransformationFactory Since the source coordinate systems doesn't have a vertical axis, height above the ellipsoid is assumed equals to zero everywhere. This method will examine the coordinate systems and delegate the work to one or many This method fails if no path between the coordinate systems is found. geotools.sourceforge.net /gt2docs/api/org/geotools/ct/CoordinateTransformationFactory.html   (654 words)

Try your search on: Qwika (all wikis)

About us   |   Why use us?   |   Reviews   |   Press   |   Contact us   Copyright © 2005-2007 www.factbites.com Usage implies agreement with terms.