scholarly journals A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

2012 ◽  
Vol 56 (4) ◽  
pp. 1791-1815 ◽  
Author(s):  
Jaroslav M. Fowkes ◽  
Nicholas I. M. Gould ◽  
Chris L. Farmer
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Continuous Functions ◽  
Branch And Bound Algorithm ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous

scholarly journals The Rate of Convergence of Lupasq-Analogue of the Bernstein Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Heping Wang ◽  
Yanbo Zhang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Bernstein Operators ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous

We discuss the rate of convergence of the Lupasq-analogues of the Bernstein operatorsRn,q(f;x)which were given by Lupas in 1987. We obtain the estimates for the rate of convergence ofRn,q(f)by the modulus of continuity off, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.

scholarly journals A new metric between distributions of point processes

2008 ◽  
Vol 40 (03) ◽  
pp. 651-672 ◽  
Author(s):  
Dominic Schuhmacher ◽  
Aihua Xia
Keyword(s):  
Point Processes ◽  
Relative Difference ◽  
Continuous Functions ◽  
Upper And Lower Bounds ◽  
Point Pattern ◽  
Multiple Point ◽  
Finite Point ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous ◽  
Comprehensive Collection

Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metric d̅ 1 that combines positional differences of points under a closest match with the relative difference in total mass in a way that fixes this flaw. A comprehensive collection of theoretical results about d̅ 1 and its induced Wasserstein metric d̅ 2 for point process distributions are given, including examples of useful d̅ 1-Lipschitz continuous functions, d̅ 2 upper bounds for the Poisson process approximation, and d̅ 2 upper and lower bounds between distributions of point processes of independent and identically distributed points. Furthermore, we present a statistical test for multiple point pattern data that demonstrates the potential of d̅ 1 in applications.

scholarly journals Imbeddings of Brezis-Wainger type. The case of missing derivatives

2001 ◽  
Vol 131 (3) ◽  
pp. 667-700
Author(s):  
M. Krbec ◽  
Hans-Jürgen Schmeisser
Keyword(s):  
Continuous Functions ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous ◽  
Mixed Derivatives

We prove limiting imbeddings of spaces with dominating mixed derivatives into the spaces of almost Lipschitz continuous functions.

scholarly journals Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Chun-Feng Wang ◽  
Yan-Qin Bai
Keyword(s):  
Global Optimization ◽  
Branch And Bound ◽  
Optimization Algorithm ◽  
Linearization Method ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Global Optimization Algorithm ◽  
Multiplicative Programming ◽  
Linear Multiplicative Programming ◽  
Pruning Techniques

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm.

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