Results 1  10
of
66
Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems
 SIAM Journal on Optimization
, 2004
"... A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the AudetDennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPSfilter algorithms for gene ..."
Abstract

Cited by 37 (8 self)
 Add to MetaCart
A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the AudetDennis Generalized Pattern Search (GPS) algorithms for bound constrained mixed variable optimization, and their GPSfilter algorithms for general nonlinear constraints. In generalizing existing algorithms, new theoretical convergence results are presented that reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are required to apply the algorithm, a hierarchy of theoretical convergence results based on the Clarke calculus is given, in which local smoothness dictate what can be proved about certain limit points generated by the algorithm. To demonstrate the usefulness of the algorithm, the algorithm is applied to the design of a loadbearing thermal insulation system. We believe this is the first algorithm with provable convergence results to directly target this class of problems.
SpaceOptimized Texture Maps
, 2002
"... Texture mapping is a common operation to increase the realism of threedimensional meshes at low cost. We propose a new texture optimization algorithm based on the reduction of the physical space allotted to the texture image. Our algorithm optimizes the use of texture space by computing a warping ..."
Abstract

Cited by 30 (0 self)
 Add to MetaCart
Texture mapping is a common operation to increase the realism of threedimensional meshes at low cost. We propose a new texture optimization algorithm based on the reduction of the physical space allotted to the texture image. Our algorithm optimizes the use of texture space by computing a warping function for the image and new texture coordinates. Neither the mesh geometry nor its connectivity are modified by the optimization. Our method uniformly distributes frequency content of the image in the spatial domain. In other words, the image is stretched in high frequency areas, whereas low frequency regions are shrunk. We also take into account distortions introduced by the mapping onto the model geometry in this process. The resulting image can be resampled at lower rate while preserving its original details. The unwarping is performed by the texture mapping function. Hence, the spaceoptimized texture is stored asis in texture memory and is fully supported by current graphics hardware. We present several examples showing that our method significantly decreases texture memory usage without noticeable loss in visual quality.
On Algorithms for Discrete and Approximate Brouwer Fixed Points
 In STOC 2005
, 2005
"... We study the algorithmic complexity of the discrete fixed point problem and develop an asymptotic matching bound for a cube in any constantly bounded finite dimension. To obtain our upper bound, we derive a new fixed point theorem, based on a novel characterization of boundary conditions for the exi ..."
Abstract

Cited by 13 (10 self)
 Add to MetaCart
We study the algorithmic complexity of the discrete fixed point problem and develop an asymptotic matching bound for a cube in any constantly bounded finite dimension. To obtain our upper bound, we derive a new fixed point theorem, based on a novel characterization of boundary conditions for the existence of fixed points. In addition, exploring a linkage with the approximation problem of the continuous fixed point problem, we obtain asymptotic matching bounds for complexity of the approximate Brouwer fixed point problem in the continuous case for Lipschitz functions that close a previous exponential gap. It settles a fifteen years old open problem of Hirsch, Papadimitriou and Vavasis by improving both the upper and lower bounds. Our new characterization for existence of a fixed point is also applicable to functions defined on nonconvex domain and makes it a potentially useful tool for design and analysis of algorithms for fixed points in general domain.
The Mathematical Import Of Zermelo's WellOrdering Theorem
 Bull. Symbolic Logic
, 1997
"... this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his wellknown paradox, an early expression of our motif. The motif becomes fully manifest through the study of functions f :
Three Metric Domains of Processes for Bisimulation
 in Proceedings of the 9th International Conference on Mathematical Foundations of Programming Semantics, LNCS
, 1993
"... A new metric domain of processes is presented. This domain is located in between two metric process domains introduced by De Bakker and Zucker. The new process domain characterizes the collection of image finite processes. This domain has as advantages over the other process domains that no complica ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
A new metric domain of processes is presented. This domain is located in between two metric process domains introduced by De Bakker and Zucker. The new process domain characterizes the collection of image finite processes. This domain has as advantages over the other process domains that no complications arise in the definitions of operators like sequential composition and parallel composition, and that image finite language constructions like random assignment can be modelled in an elementary way. As in the other domains, bisimilarity and equality coincide in this domain. The three domains are obtained as unique (up to isometry) solutions of equations in a category of 1bounded complete metric spaces. In the case the action set is finite, the three domains are shown to be equal (up to isometry). For infinite action sets, e.g., equipollent to the set of natural or real numbers, the process domains are proved not to be isometric. AMS Subject Classification (1991): 68Q55 CR Subject Classification (1991): D.3.1, F.3.2 Keywords & Phrases: process, complete metric space, bisimulation, finitely branching, image finite, sequential composition Note: This work was partially supported by the Netherlands Nationale Faciliteit Informatica programme, project Research and Education in Concurrent Systems (REX). This paper will appear in Proceedings of the Ninth Conference on the Mathematical Foundations of Programming Semantics, New Orleans, LA, USA, April 710, 1993.
Exponential Barycenters of the Canonical Cartan Connection and Invariant Means on Lie Groups
 AUTHOR MANUSCRIPT, PUBLISHED IN "MATRIX INFORMATION GEOMETRY SPRINGER (ED.) (2012)"
, 2012
"... When performing statistics on elements of sets that possess a particular geometric structure, it is desirable to respect this structure. For instance in a Lie group, it would be judicious to have a notion of a mean which is stable by the group operations (composition and inversion). Such a property ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
When performing statistics on elements of sets that possess a particular geometric structure, it is desirable to respect this structure. For instance in a Lie group, it would be judicious to have a notion of a mean which is stable by the group operations (composition and inversion). Such a property is ensured for Riemannian center of mass in Lie groups endowed with a biinvariant Riemannian metric, like compact Lie groups (e.g. rotations). However, biinvariant Riemannian metrics do not exist for most non compact and noncommutative Lie groups. This is the case in particular for rigidbody transformations in any dimension greater than one, which form the most simple Lie group involved in biomedical image registration. In this paper, we propose to replace the Riemannian metric by an affine connection structure on the group. We show that the canonical Cartan connections of a connected Lie group provides group geodesics which are completely consistent with the composition and inversion. With such
From Branching to Linear Metric Domains (and back
 6th Nordic Workshop on Programming Theory, NWPT '6 Proceedings
, 1995
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS
A fixed point theorem in a category of compact metric spaces
 Theoretical Computer Science
, 1995
"... Various results appear in the literature for deriving existence and uniqueness of fixed points for endofunctors on categories of complete metric spaces. All these results are proved for contracting functors which satisfy some further requirements, depending on the category in question. Following a n ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Various results appear in the literature for deriving existence and uniqueness of fixed points for endofunctors on categories of complete metric spaces. All these results are proved for contracting functors which satisfy some further requirements, depending on the category in question. Following a new kind of approach, based on the notion of ηisometry, we show that the sole hypothesis of contractivity is enough for proving existence and uniqueness of fixed points for endofunctors on the category of compact metric spaces and embeddingprojection pairs. 1
Computable versions of the uniform boundedness theorem
 Logic Colloquium 2002
, 2006
"... Abstract. We investigate the computable content of the Uniform Boundedness Theorem and of the closely related BanachSteinhaus Theorem. The Uniform Boundedness Theorem states that a pointwise bounded sequence of bounded linear operators on Banach spaces is also uniformly bounded. But, given the sequ ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. We investigate the computable content of the Uniform Boundedness Theorem and of the closely related BanachSteinhaus Theorem. The Uniform Boundedness Theorem states that a pointwise bounded sequence of bounded linear operators on Banach spaces is also uniformly bounded. But, given the sequence, can we also effectively find the uniform bound? It turns out that the answer depends on how the sequence is “given”. If it is just given with respect to the compact open topology (i.e. if just a sequence of “programs ” is given), then we cannot even compute an upper bound of the uniform bound in general. If, however, the pointwise bounds are available as additional input information, then we can effectively compute an upper bound of the uniform bound. Additionally, we prove an effective version of the contraposition of the Uniform Boundedness Theorem: given a sequence of linear bounded operators which is not uniformly bounded, we can effectively find a witness for the fact that the sequence is not pointwise bounded. As an easy application of this theorem we obtain a computable function whose Fourier series does not converge. §1. Introduction. In this paper we want to study the computational content of some theorems of functional analysis. The Uniform Boundedness Theorem is one of the central theorems of functional analysis and it has first been published in Banach’s thesis [1].