Filters








4,774 Hits in 7.9 sec

Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests [chapter]

Winfried Neun, Thomas Sturm, Stefan Vigerske
2010 Lecture Notes in Computer Science  
We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems.  ...  Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions.  ...  In this paper, we present a novel symbolic method to prove or disprove convexity of rational functions over polyhedral sets.  ... 
doi:10.1007/978-3-642-15274-0_19 fatcat:mkkoqo2nfbfopf6iwnycjrskbu

ON THE ACCURACY OF SOME ABSORBING BOUNDARY CONDITIONS FOR THE SCHRODINGER EQUATION

Andrej Bugajev, Raimondas Čiegis, Rima Kriauzienė, Teresė Leonavičienė, Julius Žilinskas
2017 Mathematical Modelling and Analysis  
Different strategies are investigated for the optimal selection of the coefficients of these rational functions, including the Pade approximation, the L2 norm approximations of the Fourier symbol, L2 minimization  ...  It is focused on absorbing boundary conditions that are obtained by using rational functions to approximate the exact transparent boundary conditions.  ...  Acknowledgement This research was funded by a grant (No. MIP-074/2015) from the Research Council of Lithuania.  ... 
doi:10.3846/13926292.2017.1306725 fatcat:uxjwmgaj2zgozbtisbnexpe2j4

GloptiPoly 3: moments, optimization and semidefinite programming

Didier Henrion, Jean-Bernard Lasserre, Johan Löfberg
2009 Optimization Methods and Software  
We describe a major update of our Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming.  ...  obtained by solving moment problems with test functions of increasing degrees.  ...  The gap between the lower bound and the exact minimum time is narrowed by enlarging the class of test functions g.  ... 
doi:10.1080/10556780802699201 fatcat:kigxrg76p5f2npbid42zkvwy3a

GloptiPoly 3: moments, optimization and semidefinite programming [article]

Didier Henrion, Johan Lofberg
2007 arXiv   pre-print
We describe a major update of our Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming.  ...  obtained by solving moment problems with test functions of increasing degrees.  ...  The gap between the lower bound and the exact minimum time is narrowed by enlarging the class of test functions g.  ... 
arXiv:0709.2559v1 fatcat:45guf6s5pzayvgxed4hecklptu

Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization (Dagstuhl Seminar 18081)

Pierre Bonami, Ambros M. Gleixner, Jeff Linderoth, Ruth Misener, Michael Wagner
2018 Dagstuhl Reports  
, and address numerous other applications of societal importance.  ...  The first MINLP algorithms and software were designed by application engineers.  ...  Mathematical Foundations Column generation -If we have many columns but a convex objective function, is there a notion of column generation?  ... 
doi:10.4230/dagrep.8.2.64 dblp:journals/dagstuhl-reports/BonamiGLM18 fatcat:fn6llvricbevzjsm4teuf5xuha

Optimal Designs for Rational Function Regression

Dávid Papp
2012 Journal of the American Statistical Association  
or rational weight function.  ...  The characterization is applicable to every linear model involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function.  ...  It is achieved at the price of providing numerical, rather than symbolic, solutions: the method generates the (numerical) coefficients of the sought polynomial.  ... 
doi:10.1080/01621459.2012.656035 fatcat:t7i3nmgedraslpjd6ebvyqxrma

Optimal designs for rational function regression [article]

Dávid Papp
2011 arXiv   pre-print
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial  ...  or rational weight function.  ...  It is achieved at the price of providing numerical, rather than symbolic, solutions: the method generates the (numerical) coefficients of the sought polynomial.  ... 
arXiv:1009.1444v2 fatcat:fzkcp6npwrh6bmbunu6xnsfsii

Reformulation and convex relaxation techniques for global optimization

Leo Liberti
2004 4OR  
Finally, the thesis discusses some of the software engineering issues involved in the design and implementation of codes for sBB, especially in view of the large amounts of both symbolic and numerical  ...  information required by these codes.  ...  Our analysis led us to the development of , a general software framework for optimization that can support both local and global optimization solvers.  ... 
doi:10.1007/s10288-004-0038-6 fatcat:h7ahszha7fbinnuj5zrpoa4jgm

Important moments in systems, control and optimization

Christopher I. Byrnes, Anders Lindquist
2009 Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference  
Moreover, on these spaces one can derive natural convex optimization criteria which characterize solutions to this new class of moment problems.  ...  We seek to parameterize solutions which are positive "rational" measures, in a suitably generalized sense. Our parameterization is given in terms of smooth objects.  ...  Since any open convex subset of R n is itself diffeomorphic to R n (see, e.g., [5, p. 771] ), (12) is a diffeomorphism by Hadamard's Global Inverse Function Theorem.  ... 
doi:10.1109/cdc.2009.5400258 dblp:conf/cdc/ByrnesL09 fatcat:do7vyvaubfaybocjmfdej3iho4

Exact Optimization via Sums of Nonnegative Circuits and Sums of AM/GM Exponentials [article]

Victor Magron, Henning Seidler, Timo de Wolff
2021 arXiv   pre-print
We provide two hybrid numeric-symbolic optimization algorithms, computing exact sums of nonnegative circuits (SONC) and sums of arithmetic-geometric-exponentials (SAGE) decompositions.  ...  Moreover, we provide a hybrid numeric-symbolic decision algorithm for polynomials lying in the interior of the SAGE cone.  ...  rational functions, under the assumption that the numerator belongs to the interior of the SOS cone.  ... 
arXiv:1902.02123v2 fatcat:vsekmi4jfrdati6y4tpsiwhsze

Undecidability and hardness in Mixed-Integer Nonlinear Programming

Leo Liberti
2018 Reserche operationelle  
We start by reviewing the problem of representing a solution, which is linked to the correct abstract computational model to consider.  ...  different theories, one of which is decidable while the other is not.  ...  Apparently, the unwritten standards of scientific writing, which I know and abide by, but thought could be a matter of personal choice in an invited survey, are in fact vigorously enforced (trust me).  ... 
doi:10.1051/ro/2018036 fatcat:hofoinsdazgkrgf7cjogqojuba

SOSTOOLS and Its Control Applications [chapter]

Stephen Prajna, Antonis Papachristodoulou, Peter Seiler, Pablo A. Parrilo
2005 Lecture notes in control and information sciences  
Currently, sum of squares programs are solved by casting them as semidefinite programs, which can in turn be solved using interior-point based numerical methods.  ...  Sum of squares optimization forms a basis for formulating convex relaxations to computationally hard problems such as some that appear in systems and control.  ...  There are several ways of doing this, for instance using backwards error analysis, or by computing rational solutions, that we can fully verify symbolically.  ... 
doi:10.1007/10997703_14 fatcat:z6el4lkwpbh2fj6zqie3zqauiu

Exact Optimization via Sums of Nonnegative Circuits and Arithmetic-geometric-mean-exponentials

Victor Magron, Henning Seidler, Timo de Wolff
2019 Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation - ISSAC '19  
We provide two hybrid numeric-symbolic optimization algorithms, computing exact sums of nonnegative circuits (SONC) and sums of arithmetic-geometricexponentials (SAGE) decompositions.  ...  Moreover, we provide a hybrid numeric-symbolic decision algorithm for polynomials lying in the interior of the SAGE cone.  ...  rational functions, under the assumption that the numerator belongs to the interior of the SOS cone.  ... 
doi:10.1145/3326229.3326271 dblp:conf/issac/MagronSW19 fatcat:f5kmuwo7xneuxb7one733vnbli

Duality of sum of nonnegative circuit polynomials and optimal SONC bounds [article]

Dávid Papp
2019 arXiv   pre-print
The method is implemented and tested on a large set of sparse polynomial optimization problems with up to 40 unknowns, of degree up to 60, and up to 3000 monomials in the support.  ...  Our proof, based on convex programming duality, removes the nondegeneracy assumption and motivates an algorithm that generates an optimal set of circuits and computes the corresponding SONC bound in a  ...  The author is grateful to Mareike Dressler (UCSD) for pointing out the reference to Jie Wang's recent work [37] on the support of SONC polynomials.  ... 
arXiv:1912.04718v1 fatcat:fes5gx4p6vfwbkmrgocgtrobli

Computing sum of squares decompositions with rational coefficients

Helfried Peyrl, Pablo A. Parrilo
2008 Theoretical Computer Science  
Sum of squares (SOS) decompositions for nonnegative polynomials are usually computed numerically, using convex optimization solvers.  ...  In this paper, we present a numeric-symbolic method that exploits the efficiency of numerical techniques to obtain an approximate solution, which is then used as a starting point for the computation of  ...  The problem is convex since its objective function and the feasible region defined by the constraints are convex.  ... 
doi:10.1016/j.tcs.2008.09.025 fatcat:alp6ey5pgjeopixb3r5iaj2ikm
« Previous Showing results 1 — 15 out of 4,774 results