An existence level for the residual sum of squares of the power-law regression with an unknown location parameter

2021 ◽  
Vol 71 (4) ◽  
pp. 1019-1026
Author(s):  
Dragan Jukić ◽  
Tomislav Marošević
Keyword(s):  
Power Law ◽  
Bounded Function ◽  
Location Parameter ◽  
Sum Of Squares ◽  
Necessary And Sufficient Condition ◽  
Global Minima ◽  
Sufficient Criterion ◽  
Least Squares Estimate ◽  
Necessary And Sufficient ◽  
Appl Math

Abstract In a recent paper [JUKIĆ, D.: A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set, J. Comput. Appl. Math. 375 (2020)], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.

EQUIVALENT SEQUENTIAL AND PARALLEL REDUCTIONS IN ARBITRARY BINARY PICTURES

2014 ◽  
Vol 28 (07) ◽  
pp. 1460009 ◽  
Author(s):  
KÁLMÁN PALÁGYI
Keyword(s):  
Single Point ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sufficient Criterion ◽  
Translation Invariant ◽  
Necessary And Sufficient

A reduction transforms a binary picture only by changing some black points to white ones, which is referred to as deletion. Sequential reductions traverse the black points of a picture, and consider a single point for possible deletion, while parallel reductions can delete a set of black points simultaneously. Two reductions are called equivalent if they produce the same result for each input picture. A deletion rule is said to be equivalent if it yields a pair of equivalent parallel and sequential reductions. This paper introduces a class of equivalent deletion rules that allows us to establish a new sufficient condition for topology-preserving parallel reductions in arbitrary binary pictures. In addition we present a method of verifying that a deletion rule given by matching templates is equivalent, a necessary and sufficient condition for order-independent deletion rules, and a sufficient criterion for order-independent and translation-invariant parallel subfield-based algorithms.

TUNING STRATEGIES IN CONSTRAINED SIMULATED ANNEALING FOR NONLINEAR GLOBAL OPTIMIZATION

2000 ◽  
Vol 09 (01) ◽  
pp. 3-25 ◽  
Author(s):  
BENJAMIN W. WAH ◽  
TAO WANG
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Mixed Integer ◽  
Asymptotic Convergence ◽  
Necessary And Sufficient Condition ◽  
Global Minima ◽  
Global Optimization Algorithm ◽  
Constrained Simulated Annealing ◽  
Cooling Schedules ◽  
Necessary And Sufficient

This paper studies various strategies in constrained simulated annealing (CSA), a global optimization algorithm that achieves asymptotic convergence to constrained global minima (CGM) with probability one for solving discrete constrained nonlinear programming problems (NLPs). The algorithm is based on the necessary and sufficient condition for discrete constrained local minima (CLM) in the theory of discrete Lagrange multipliers and its extensions to continuous and mixed-integer constrained NLPs. The strategies studied include adaptive neighborhoods, distributions to control sampling, acceptance probabilities, and cooling schedules. We report much better solutions than the best-known solutions in the literature on two sets of continuous benchmarks and their discretized versions.

A Necessary and Sufficient Condition for the Genericity of Serial Manipulators

2007 ◽  
Author(s):  
Andreas Mu¨ller
Keyword(s):  
Tangent Space ◽  
Smooth Manifold ◽  
Maximal Rank ◽  
Sufficient Condition ◽  
Singular Set ◽  
Necessary And Sufficient Condition ◽  
Redundant Manipulator ◽  
Sufficient Criterion ◽  
Serial Manipulators ◽  
Necessary And Sufficient

Transverse-regularity is a point-wise manipulator property, ensuring that the singular set Σ is locally a smooth manifold. A generic manipulator is one which is transverse-regular in any configuration. The contribution of this paper is a necessary and sufficient condition for transverse-regularity. The condition is based on the manipulator’s joint screws and their screw products. An expression for the tangent space to Σ at transverse-regular singularities is derived. It is shown that a manipulator is non-generic if it can attain a pose where the rank of the manipulator’s screw system together with the screw products is not the maximal rank of the Jacobian. A necessary and sufficient criterion for degree-one singularities is given in terms of the mechanism’ joint screws. In particular, any non-redundant manipulator is transverse-regular in a degree-one singularity.

scholarly journals A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 166
Author(s):  
Xiaojie Dou  ◽  
Jin-San Cheng 
Keyword(s):  
Real Zero ◽  
Heuristic Method ◽  
Polynomial Systems ◽  
Sum Of Squares ◽  
Interval Methods ◽  
Necessary And Sufficient Condition ◽  
Real Zeros ◽  
Input System ◽  
Necessary And Sufficient ◽  
The Given

In this paper, by transforming the given over-determined system into a square system, we prove a necessary and sufficient condition to certify the simple real zeros of the over-determined system by certifying the simple real zeros of the square system. After certifying a simple real zero of the related square system with the interval methods, we assert that the certified zero is a local minimum of sum of squares of the input polynomials. If the value of sum of squares of the input polynomials at the certified zero is equal to zero, it is a zero of the input system. As an application, we also consider the heuristic verification of isolated zeros of polynomial systems and their multiplicity structures.

On the 𝐿1-Convergence of Modified Cosine Sums

2008 ◽  
Vol 15 (1) ◽  
pp. 71-75
Author(s):  
Karanvir Singh ◽  
Kulwinder Kaur
Keyword(s):  
Indian Acad ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Cosine Series ◽  
Necessary And Sufficient ◽  
Appl Math

Abstract Concerning the 𝐿1-convergence of modified cosine sums introduced by Kumari and Ram [Indian J. Pure Appl. Math. 19: 1101–1104, 1988], we generalise the results of Kumari, Ram [Indian J. Pure Appl. Math. 19: 1101–1104, 1988] and Bor [Proc. Indian Acad. Sci. Math. Sci. 102: 235–238, 1992]. Also a necessary and sufficient condition for the 𝐿1-convergence of cosine series has been deduced as a corollary for the said class.

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