Quasiconvex optimization for robust geometric reconstruction 2005 12 citations ? 1 self

es maxi fi(x) Convex pro![rams are quasiconvex pro![rams Convex objective function is quasiconvex Replace each linear inequality constraint by a step function Very high value where constraint violated Very small value where constraint satisfied Quasiconvex pro![rams are ![eneralized linear pro![rams Define f(S) = maxims fi(x) satisfies a[[ the GLP axioms He[[y's theorem ives bounds on GLP dimension (cardinality of basis): at most 2d+1 for arbitrary quasiconvex proram at most d+l for we[I-behaved quasiconvex functions ([eve[ sets strictly nested...

es maxi fi(x) Convex pro![rams are quasiconvex pro![rams Convex objective function is quasiconvex Replace each linear inequality constraint by a step function Very high value where constraint violated Very small value where constraint satisfied Quasiconvex pro![rams are ![eneralized linear pro![rams Define f(S) = maxims fi(x) satisfies a[[ the GLP axioms He[[y's theorem ives bounds on GLP dimension (cardinality of basis): at most 2d+1 for arbitrary quasiconvex proram at most d+l for we[I-behaved quasiconvex functions ([eve[ sets strictly nested...

Abstract. We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either numerically or via generalizations of the dual simplex method from linear programming, and describe varied applications of this geometric optimization technique in meshing, scientific computation, information visualization, automated algorithm analysis, and robust statistics. 1.

. We study the stability problem of the quasiconvex hull Q(K) for a compact set K ae M N \Thetan with respect to K by using Hausdorff metric over compact sets. We introduce various stability criteria and examine some examples including the quasiconvex hull for the two-well problem in modelling martensitic phase transformations. x1. Introduction. In this paper we use the Hausdorff metric on space of compact subsets in M N \Thetan (the space of N \Theta n real matrices) to study the stability of quasiconvex hulls. We introduce various stability c...

Dedicated to my mother, Margarita, and my brother, Vardan. ii ACKNOWLEDGMENTS I would like to express my gratitude to the people who helped me on the way to writing this thesis. First of all, I thank my family for the care and support you provided for all these years. Your encouragement is the very reason why this work exists. I am deeply indebted to my advisor, Professor Alexander Ol?shanskii, for his guidance, help and patience during my studies at the Moscow State University and Vanderbilt. Doctor Ol?shanskii has been directing my research f...

Abstract Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex formulation. Based on the quasiconvexity, we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small-scale convex programs that are ready to solve. Our final ...

We show that the Steepest Descent Algorithm in connection with wiggly energies yields minimizing sequences that converge to a global minimum of the associated non-quasiconvex variational integrals. We introduce a multi-level infinite dimensional variant of the Steepest Descent Algorithm designed to compute complex microstructures by forming non-smooth minimizers from the smooth initial guess. We apply this multilevel method to the minimization of the variational problems associated with martensitic branching. Keywords Quasiconvexity, nonconvex ...

Abstract. We review various sorts of generalized convexity and we raise some questions about them. We stress the importance of some special subclasses of quasiconvex functions. Dedicated to Marc Att?ia R?sum?. Nous passons en revue quelques notions de convexit? g?n?ralis?e. Nous tentons de les relier et nous soulevons quelques questions. Nous soulignons l?importance de quelques classes particuli?res de fonctions quasiconvexes. 1.

Abstract Geometric reconstruction problems in computer vision can be solved by minimizing the maximum of reprojection errors, i.e., the Linfty-norm. Unlike L2-norm (sum of squared reprojection errors), the global minimum of Linfty-norm can be efficiently achieved by quasiconvex optimization. However, the maximum of reprojection errors is the meaningful measure to minimize only when the measurement noises are independent and identically distributed at every 2D feature point and in both directions in the image. This is rarely the case in real da...

Abstract Uncertainty tolerance and H?? attenuations are two important concerns in feedback control design. It is therefore important to develop effective methods to compute the trade-off between these two objectives. Using quasiconvex optimization approach, this paper develops algorithms for two problems in this regard: 1) given the uncertainty size of the system, compute the minimum H?? norm bound of the closed loop system reachable by state feedback control; and 2) given the required maximum acceptable H?? norm bound of the closed loop syste...

www.TheDCAsite.com http www.nature.com www.depmed.ualberta.ca BREAKING NEWS - CANCER CURE FOUND! CAN...

.skepticsannotate... Foundation for Freedom of Expression http om.html Faith Freedom International w...