Weisfeiler-Lehman Refinement Requires at Least a Linear Number of Iterations

The dual formulation of support vector regression involves two closely related sets of variables. When the decomposition method is used, many existing approaches use pairs of indices from these two sets as the working set. Basically, they select a base set first and then expand it so all indices are pairs. This makes the implementation different from that for support vector classification. In addition, a larger optimization subproblem has to be solved in each iteration. We provide theoretical proofs and conduct experiments to show that using the base set as the working set leads to similar convergence (number of iterations). Therefore, by using a smaller working set while keeping a similar number of iterations, the program can be simpler and more efficient.

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On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

Entropy ◽

10.3390/e23040465 ◽

2021 ◽

Vol 23 (4) ◽

pp. 465

Author(s):

Agnieszka Prusińska ◽

Krzysztof Szkatuła ◽

Alexey Tret’yakov

Keyword(s):

Computational Complexity ◽

Polynomial Complexity ◽

Initial Point ◽

Quadratic Functions ◽

Problem Dimension ◽

Piecewise Quadratic Functions ◽

Large Systems ◽

Systems Of Linear Inequalities ◽

Number Of Iterations ◽

Finite Number Of Iterations

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.

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A Comparative Study among New Hybrid Root Finding Algorithms and Traditional Methods

Mathematics ◽

10.3390/math9111306 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1306

Author(s):

Elsayed Badr ◽

Sultan Almotairi ◽

Abdallah El Ghamry

Keyword(s):

Comparative Study ◽

Numerical Results ◽

Traditional Methods ◽

Running Time ◽

Root Finding ◽

Average Running Time ◽

False Position ◽

Newton Raphson ◽

Number Of Iterations

In this paper, we propose a novel blended algorithm that has the advantages of the trisection method and the false position method. Numerical results indicate that the proposed algorithm outperforms the secant, the trisection, the Newton–Raphson, the bisection and the regula falsi methods, as well as the hybrid of the last two methods proposed by Sabharwal, with regard to the number of iterations and the average running time.

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A Termination Criterion for Probabilistic Point Clouds Registration

Signals ◽

10.3390/signals2020013 ◽

2021 ◽

Vol 2 (2) ◽

pp. 159-173

Author(s):

Simone Fontana ◽

Domenico Giorgio Sorrenti

Keyword(s):

State Of The Art ◽

Point Clouds ◽

Computational Time ◽

Termination Criteria ◽

Practical Usefulness ◽

Local Point ◽

Termination Criterion ◽

Probabilistic Point ◽

Excessive Number ◽

Number Of Iterations

Probabilistic Point Clouds Registration (PPCR) is an algorithm that, in its multi-iteration version, outperformed state-of-the-art algorithms for local point clouds registration. However, its performances have been tested using a fixed high number of iterations. To be of practical usefulness, we think that the algorithm should decide by itself when to stop, on one hand to avoid an excessive number of iterations and waste computational time, on the other to avoid getting a sub-optimal registration. With this work, we compare different termination criteria on several datasets, and prove that the chosen one produces very good results that are comparable to those obtained using a very large number of iterations, while saving computational time.

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Scanning integer points with lex-inequalities: a finite cutting plane algorithm for integer programming with linear objective

4OR ◽

10.1007/s10288-020-00459-6 ◽

2020 ◽

Author(s):

Michele Conforti ◽

Marianna De Santis ◽

Marco Di Summa ◽

Francesco Rinaldi

Keyword(s):

Integer Point ◽

Cutting Plane ◽

Integer Program ◽

Compact Set ◽

Cutting Plane Method ◽

Integer Points ◽

Gomory Cuts ◽

The Family ◽

Split Cuts ◽

Number Of Iterations

AbstractWe consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that define the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-inequalities contains the Chvátal–Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program $$\min \{cx: x\in S\cap \mathbb {Z}^n\}$$ min { c x : x ∈ S ∩ Z n } , where $$S\subset \mathbb {R}^n$$ S ⊂ R n is a compact set and $$c\in \mathbb {Z}^n$$ c ∈ Z n . We analyze the number of iterations of our algorithm.

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Converting MST to TSP Path by Branch Elimination

Applied Sciences ◽

10.3390/app11010177 ◽

2020 ◽

Vol 11 (1) ◽

pp. 177

Author(s):

Pasi Fränti ◽

Teemu Nenonen ◽

Mingchuan Yuan

Keyword(s):

Spanning Tree ◽

Closed Loop ◽

Minimum Spanning Tree ◽

Travelling Salesman Problem ◽

Open Loop ◽

Travelling Salesman ◽

Elimination Algorithm ◽

Number Of Iterations ◽

Number Of Branches

Travelling salesman problem (TSP) has been widely studied for the classical closed loop variant but less attention has been paid to the open loop variant. Open loop solution has property of being also a spanning tree, although not necessarily the minimum spanning tree (MST). In this paper, we present a simple branch elimination algorithm that removes the branches from MST by cutting one link and then reconnecting the resulting subtrees via selected leaf nodes. The number of iterations equals to the number of branches (b) in the MST. Typically, b << n where n is the number of nodes. With O-Mopsi and Dots datasets, the algorithm reaches gap of 1.69% and 0.61 %, respectively. The algorithm is suitable especially for educational purposes by showing the connection between MST and TSP, but it can also serve as a quick approximation for more complex metaheuristics whose efficiency relies on quality of the initial solution.

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Multiple returns under a bounded number of iterations

Theoretical Computer Science ◽

10.1016/0304-3975(94)90074-4 ◽

1994 ◽

Vol 123 (1) ◽

pp. 139-144

Author(s):

Zbigniew S. Kowalski

Keyword(s):

Bounded Number ◽

Number Of Iterations

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A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm

Advances in Agriculture ◽

10.1155/2016/2313695 ◽

2016 ◽

Vol 2016 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Godfrey Chagwiza ◽

Chipo Chivuraise ◽

Christopher T. Gadzirayi

Keyword(s):

Integer Programming ◽

Mixed Integer Programming ◽

Moringa Oleifera ◽

Bat Algorithm ◽

Mixed Integer ◽

Poultry Feed ◽

Integer Programming Problem ◽

Optimum Solution ◽

Mixed Integer Programming Problem ◽

Number Of Iterations

In this paper, a feed ration problem is presented as a mixed integer programming problem. An attempt to find the optimal quantities of Moringa oleifera inclusion into the poultry feed ration was done and the problem was solved using the Bat algorithm and the Cplex solver. The study used findings of previous research to investigate the effects of Moringa oleifera inclusion in poultry feed ration. The results show that the farmer is likely to gain US$0.89 more if Moringa oleifera is included in the feed ration. Results also show superiority of the Bat algorithm in terms of execution time and number of iterations required to find the optimum solution as compared with the results obtained by the Cplex solver. Results revealed that there is a significant economic benefit of Moringa oleifera inclusion into the poultry feed ration.

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A Method for Computing the Number of Iterations in Data Dependent Loops

Real-Time Systems ◽

10.1007/s11241-006-5317-1 ◽

2006 ◽

Vol 32 (1-2) ◽

pp. 73-104 ◽

Cited By ~ 3

Author(s):

Francesco Curatelli ◽

Leonardo Mangeruca

Keyword(s):

Number Of Iterations

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ANALYSIS OF PARSING AND WEBSCRAPING TOOLS WITHIN THE FRAMEWORK DEVELOPMENT OF ARBITRATION INVESTMENT STRATEGY ON THE MARKET SPORT BETS

SOFT MEASUREMENTS AND COMPUTING ◽

10.36871/2618-9976.2021.02.006 ◽

2021 ◽

Vol 1 (2) ◽

pp. 65-77

Author(s):

T. E. Vildanov ◽

◽

N. S. Ivanov ◽

Keyword(s):

Data Extraction ◽

Investment Strategy ◽

Semistructured Data ◽

Graphical Form ◽

Great Demand ◽

Rapid Extraction ◽

Web Scraping ◽

Quantitative Metrics ◽

Framework Development ◽

Number Of Iterations

This article explores both popular and newly invented tools for extracting data from sites and converting them into a form suitable for analysis. The paper compares the Python libraries, the key criterion of the compared tools is their performance. The results will be grouped by sites, tools used and number of iterations, and then presented in graphical form. The scientific novelty of the research lies in the field of application of data extraction tools: we will receive and transform semistructured data from the websites of bookmakers and betting exchanges. The article also describes new tools that are currently not in great demand in the field of parsing and web scraping. As a result of the study, quantitative metrics were obtained for all the tools used and the libraries that were most suitable for the rapid extraction and processing of information in large quantities were selected.

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