MATHEMATICAL MODELING OF OPTIMAL HEIGHTS OF EXTERNAL GEODESIC SIGNS
Due to the great importance of geodetic networks for the formation of a unified coordinate system on the territory of Ukraine, external geodetic signs have been established, which need to be restored and further developed. At the design stage, the calculation of the heights of geodetic signs is performed on topographic maps. The cost of erection of geodetic signs on average is 50 - 60% of the total cost of creating a geodetic network, so there is a need to pay close attention to the choice of places to build signs that provide their optimal height. The article presents a methodical approach to determining the heights of external geodetic signs, based on the mathematical apparatus used for modeling and solving optimization problems. The principle of construction of the optimization model of the problem during the design of external geodetic signs in the conditions when their direct visibility should be provided is considered. The article considers in detail the types and structures of external geodetic signs, identifies the features of their location and construction. The resulting optimization model includes objective function, which is a quadratic form, and line restriction. This model is a model of quadratic programming, that belongs to a class of nonlinear programming models, but have their particular case and the simplest of nonlinear. This is because property quadratic model, which consists in the fact that since the problem of quadratic programming set of feasible solutions is convex, then, if the objective function is concave, any local maximum is global, and if the objective function is convex, then any local minimum is also global. The necessity of solving the problem of optimizing the heights of geodetic signs is substantiated, which is still connected with the financial costs for their construction and reconstruction. It is concluded that the approach to determining the heights of external geodetic signs presented in the article, which uses a mathematical apparatus for solving optimization problems, is an effective and efficient approach, and allows to numerically justify the minimum required and sufficient height of external geodetic signs. Using the present approach to the determination of geodetic heights external signs to optimize the financial costs of their construction, which is essential.
Kushtin I.F. Geodeziya : ucheb.-prakt. pos. – Moskva : «Izdatel'stvo PRIOR», 2001. – 448 s.
Derzhavna heodezychna merezha Ukrainy [Elektronnyi resurs] / Derzhavna sluzhba Ukrainy z pytan heodezii, kartohrafii ta kadastru. Naukovo-doslidnyi instytut heodezii i kartohrafii. – Rezhym dostupu: http://dgm.gki.com.ua/
Romanyshyn P.O. Rozvytok astronomo-heodezychnoi merezhi Ukrainy / P.O. Romanyshyn, A.O. Teliatnyk, I.M. Zaiets // Visnyk heodezii ta kartohrafii. – Kyiv, 1994. – № 1.
Bondar A.L. Stan ta osnovni napriamy rozvytku derzhavnoi heodezychnoi merezhi Ukrainy / A.L. Bondar, I.M. Zaiets, O.V. Kucher // Visnyk heodezii ta kartohrafii. – Kyiv, 2001. – № 3.
Pro derzhavnyi zemelnyi kadastr : Zakon Ukrainy vid 16.10.2012 r. № 5462–VI // Vidomosti Verkhovnoi Rady Ukrainy. – 2012. – № 8. – st. 61.
Zaiets I. Osoblyvosti zahalnoho vyrivniuvannia derzhavnoi heodezychnoi merezhi Ukrainy / I. Zaiets // Heodeziia i heodynamika: Suchasni dosiahnennia heodezychnoi nauky ta vyrobnytstva. – Lviv, 2013. – Vyp. 1 (25). – S. 43–50.
Monitorynh stanu punktiv heodezychnoi merezhi Ukrainy z vykorystanniam sotsialnykh merezh [Elektronnyi resurs]. – Rezhym dostupu : http://ena.lp.edu.ua/bitstream/ntb/34313/1/06_35-37.pdf
Michal, Ondrej. (2016). OPTIMIZATION METHODS IN GEODETIC NETWORKS / 16th International Multidisciplinary Scientific GeoConference SGEM 2016, www.sgem.org, SGEM2016 Conference Proceedings, ISBN 978-619-7105-59-9 / ISSN 1314-2704, June 28 - July 6, 2016, Book2 Vol. 2, 479–486 pp.
Heodezychnyi entsyklopedychnyi slovnyk / Za redaktsiieiu V. Litynskoho. – Lviv: Yevrosvit, 2001. – 668 s.
Instruktsiia z topohrafichnoho znimannia u masshtabakh 1:5 000, 1:2 000, 1:1 000 ta 1:500, (HKNTA-2.04-02-98) / Ukrheodezkartohrafiia, 1999 r. Dokument z0393-98, potochna redaktsiia. – Rezhym dostupu : https://zakon.rada.gov.ua/laws/show/z0393-98/
Ehkonomiko-matematicheskie metody : ehl. ucheb. [Elektronnyi resurs]. – Rezhym dostupu : http://www.math.mrsu.ru/text/courses/method/kvadratichnoe_programmirovanie.htm
Teoriya i metody resheniya zadach nevypuklogo kvadratichnogo programmirovaniya. [Elektronnyi resurs]. – Rezhym dostupu : https://www.rfbr.ru/rffi/ru/project_search/o_73804
Tatarenko S.I. Linejnoe reshenie zadachi kvadratichnogo programmirovaniya / S.I. Tatarenko // Programmnye produkty i sistemy. – 2014. – № 3(107), S. 36–40. – Rezhym dostupu : https://cyberleninka.ru/article/n/lineynoe-reshenie-zadachi-kvadratichnogo-programmirovaniya
The authors who publish in this collection agree with the following terms:
• The authors reserve the right to authorship of their work and give the magazine the right to first publish this work under the terms of license CC BY-NC-ND 4.0 (with the Designation of Authorship - Non-Commercial - Without Derivatives 4.0 International), which allows others to freely distribute the published work with a mandatory reference to the authors of the original work and the first publication of the work in this magazine.
• Authors have the right to make independent extra-exclusive work agreements in the form in which they were published by this magazine (for example, posting work in an electronic repository of an institution or publishing as part of a monograph), provided that the link to the first publication of the work in this journal is maintained. .
• Journal policy allows and encourages the publication of manuscripts on the Internet (for example, in institutions' repositories or on personal websites), both before the publication of this manuscript and during its editorial work, as it contributes to the emergence of productive scientific discussion and positively affects the efficiency and dynamics of the citation of the published work (see The Effect of Open Access).