The problems of non-convex quadratic programming related to phased antenna~arrays~optimization

N. N. Tyunin

Diskretnyj analiz i issledovanie operacij, Tome 28 (2021) no. 3, pp. 65-89.

Résumé

The problem of short wave phased antenna arrays optimization was formulated as a quadratic programming problem. A penalty functions method and gradient ascent algorithm were applied to analyze a structure of a local optima set. The results of the proposed algorithm were compared with the results of the well-known BARON solver. Tab. 2, illustr. 3, bibliogr. 32.

Détail

Keywords: quadratic programming, local optimum, antenna array, gradient optimization, computational experiment.

Bibliographie

[1] Hansen R. C., Phased array antennas, Wiley, Hoboken, NJ, 2009, 580 pp.

[2] Kudzin V. P., Lozovsky V. N., Shlyk N. I., “The compact linear antenna array system of the short-wave band consisting of «butterfly» radiators”, Proc. IX Int. Conf. Antenna Theory and Techniques (Odessa, Ukraine, Sept. 16–20, 2013), IEEE, Piscataway, 2013, 252–253

[3] Wilensky R., “High-power, broad-bandwidth HF dipole curtain array with extensive vertical and azimuthal beam control”, IEEE Trans. Broadcast., 34:2 (1988), 201–209

[4] Yin Ya., Deng J., “Design of short wave communication system with phased array antenna”, Electron. Eng., 33:9 (2007), 31–33 (Chinese)

[5] D. M. Sazonov, Antennas and Microwave Devices, Vysshaya Shkola, M., 1988 (Russian)

[6] Indenbom M., Izhutkin V., Sharapov A., Zonov A., “Synthesis of conical phased antenna arrays optimization of amplitude distribution parameters”, Proc. IX Int. Conf. Optimization and Applications (Petrovac, Montenegro, Oct. 1–5, 2018), DEStech Publ., Lancaster, PA, 2018, 273–285

[7] Fuchs B., “Application of convex relaxation to array synthesis problems”, IEEE Trans. Antennas Propag., 62:2 (2014), 634–640

[8] Akdagli A., Guney K., “Shaped-beam pattern synthesis of equally and unequally spaced linear antenna arrays using a modified tabu search algorithm”, Microw. Opt. Technol. Lett., 36:1 (2003), 16–20

[9] Boriskin A. V., Balaban M. V., Galan O. Yu., Sauleau R., “Efficient approach for fast synthesis of phased arrays with the aid of a hybrid genetic algorithm and a smart feed representation”, Proc. 2010 IEEE Int. Symp. Phased Array Systems and Technology (Waltham, MA, USA, Oct. 12–15, 2010), IEEE, Piscataway, 2010, 827–832

[10] Akdagli A., Guney K., “Parallel genetic-algorithm optimization of shaped beam coverage areas using planar 2-D phased arrays”, IEEE Trans. Antennas Propag., 55:6 (2007), 1745–1753

[11] A. S. Yurkov, Optimization of Excitation of Transmitting Phased Antenna Arrays of Decameter Wavelength Range, ONIIP, Omsk, 2014 (Russian)

[12] A. S. Yurkov, “Maximizing the directivity of shortwave phased array antennas”, Tech. Radiosvyazi, 2016, no. 2, 46–53 (Russian)

[13] Obukhovets V A., “Antenna array iterative synthesis algorithm” (Divnomorskoe, Krasnodar Reg., Russia, June 26–30, 2017), Proc. 2017 Radiation and Scattering of Electromagnetic Waves, 2017, 58–60, IEEE, Piscataway

[14] Echeveste J. I., de Aza M. G., Zapata J., “Shaped beam synthesis of real antenna arrays via finite-element method, floquet modal analysis, and convex programming”, IEEE Trans. Antennas Propag., 64:4 (2016), 1279–1286 | Zbl

[15] Murty K., “Some NP-complete problems in quadratic and nonlinear programming”, Math. Program., 39 (1987), 117–129 | Zbl

[16] Yu. E. Nesterov, Introduction to Convex Optimization, MTsNMO, M., 2010 (Russian)

[17] Ryoo H. S., Sahinidis N. V., “Global optimization of nonconvex NLPs and MINLPs with applications in process design”, Comput. Chem. Eng., 19:5 (1995), 551–566

[18] A. V. Eremeev, K. R. Rives, “Confidence intervals for the number of local optima”, Mat. Strukt. Model., 2017, no. 41, 55–74 (Russian) | Zbl

[19] A. S. Yurkov, “On the influence of losses in the ground on the operation of the four-element PAA HF range”, Tech. Radiosvyazi, 2014, no. 1, 78–81 (Russian)

[20] Burke J. J., Poggio A. J., Numerical electromagnics code, Lawrence Livermore Nat. Lab., Livermore, CA, 1981 (accessed March 11, 2021) https://www.nec2.org

[21] Horst R., Tuy H., Global optimization: Deterministic approaches, Springer, Heidelberg, 1996, 730 pp. | Zbl

[22] Tawarmalani M., Sahinidis N. V., “Global optimization of mixed-integer nonlinear programs: A theoretical and computational study”, Math. Program., 99:3 (2004), 563–591 | Zbl

[23] Handbook of global optimization, Nonconvex Optim. Its Appl., 2, Kluwer Acad. Publ., Dordrecht, 1995, 880 pp. | Zbl

[24] Strekalovsky A. S., “Global optimality conditions in nonconvex optimization”, J. Optim. Theory Appl., 173:3 (2017), 770–792 | Zbl

[25] Himmelblau D. M., Applied nonlinear programming, McGraw-Hill, New York, 1972, 498 pp. | Zbl

[26] Kennedy J., Eberhart R., “Particle swarm optimization”, Proc. Int. Conf. Neural Networks (Perth, Australia, Nov. 27–Dec. 1, 1995), v. 4, IEEE, Piscataway, 1995, 1942–1948

[27] Storn R., Price K., “Differential evolution — a simple and efficient heuristic for global optimization over continuous spaces”, J. Global Optim., 11:4 (1997), 341–359 | Zbl

[28] Horn R. A., Johnson C. R., Matrix analysis, Camb. Univ. Press, New York, 1990, 561 pp. | Zbl

[29] V. V. Eryomin, N. N. Astafiev, Introduction to the Theory of Linear and Convex Programming, Nauka, M., 1976 (Russian)

[30] Aoki M., Introduction to optimization techniques: Fundamentals and applications of nonlinear programming, Macmillan, New York, 1971, 335 pp. | Zbl

[31] Tawarmalani M., Sahinidis N. V., “Global optimization of mixed-integer nonlinear programs: A theoretical and computational study”, Math. Program., 99:3 (2004), 563–591 | Zbl

[32] Eremeev A. V., Yurkov A. S., “On symmetry groups of some quadratic programming problems”, Mathematical Optimization Theory and Operations Research, Proc. 19th Int. Conf. MOTOR 2020 (Novosibirsk, Russia, July 6–10, 2020), Lect. Notes Comput. Sci., 12095, Springer, Cham, 2020, 35–48 | Zbl