Abstract
One common form of optimization is convex programming that has a wide range of applications in all fields of engineering, in particular electrical engineering. This kind of programming is characterized by some conditions and properties in the construction of functions used in the objective and constraints functions. One major advantage of convex programming is that any local optimal point is also global, which brings forward a great step in the algorithms to solve convex optimization problems. This chapter first defines convex sets and convex functions, using which the definitions of convex and geometric programming problems are determined. To clarify these definitions, appropriate application examples in electrical engineering are given accordingly.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge, Cambridge University Press, 2004)
H. Hindi, A tutorial on convex optimization ii: duality and interior point methods, in Proceedings of the American Control Conference, 2006
H. Hindi, A tutorial on convex optimization, in Proceedings of the American Control Conference, 2004
Y. Nesterov, A. Nemirovsky, Interior Point Polynomial Algorithms in Convex Programming (SIAM, Philadelphia, 1994)
M.S. Bazaraa, J.J. Jarvis, H.D. Sherali, Linear Programming and Network Flows (Wiley, Hoboken, 2009)
S. Boyda, S.J. Kim, L. Vandenberghe, A. Hassibi, A tutorial on geometric programming. Optim. Eng. 8(1), 67–127 (2007)
K.O. Kortanek, X. Xu, Y. Ye, An infeasible interior-point algorithm for solving primal and dual geometric programs. Math. Program. 76(1), 155–181 (1996)
Z.-Q. Luo, W. Yu, An introduction to convex optimization for communications and signal processing. IEEE J. Sel. Areas Commun. 24, 1426–1438 (2006)
J.A. Taylor, Convex Optimization of Power Systems (Cambridge University Press, Cambridge, 2015)
M. Grant, S. Boyd, CVX: Matlab software for disciplined convex programming, version 2.1 (2014). http://cvxr.com/cvx
GNU linear programming kit, Version 4.45. http://www.gnu.org/software/glpk
MOSEK, Mosek optimization toolbox (2002). www.mosek.com
W. Stanczak, M. Wiczanowski, H. Boche, Fundamentals of Resource Allocation in Wireless Networks: Theory and Algorithms (Springer, Berlin, 2008)
S. Kandukuri, S. Boyd, Optimal power control in interference limited fading wireless channels with outage probability specifications. IEEE Trans. Wirel. Commun. 1, 46–55 (2002)
H. Bevrani, B. Francoist, T. Ise, Microgrid Dynamics and Control (Wiley, Hoboken, 2017)
H. Bevrani, M. Watanabe, Y. Mitani, Power System Monitoring and Control (IEEE-Wiley, Hoboken, 2014)
M. Fathi, H. Bevrani, Regulating power management in interconnected microgrids. J. Renew. Sust. Energy 9, 055502 (2017)
M. Fathi, H. Bevrani, Adaptive energy consumption scheduling for connected microgrids under demand uncertainty. IEEE Trans. Power Deliv. 28, 1576–1583 (2013)
M. Fathi, H. Bevrani, Statistical cooperative power dispatching in interconnected microgrids. IEEE Trans. Sust. Energy 4, 586–593 (2013)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Fathi, M., Bevrani, H. (2019). Convex Programming. In: Optimization in Electrical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-05309-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-05309-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05308-6
Online ISBN: 978-3-030-05309-3
eBook Packages: EngineeringEngineering (R0)