Abstract
Almost all useful optimization problems have more than one design variable, so it’s important to understand methods that work for any number of variables. Conveniently, some of these methods are just extensions of single-variable methods. The methods in this chapter are not hard to implement and some equivalent functions are available in MATLAB. We will focus on two variable problems since they can be represented using surface or contour plots. However, methods that work for two design variables generally work for any larger number of design variables as well.
Continuous improvement is better than delayed perfection
-Mark Twain
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kreszig E (2011) Advanced engineering mathematics, 10th edn. Wiley, Hoboken
Hamming R (1987) Numerical methods for scientists and engineers. Dover, Mineola
Sendeckyj G (1990) Interviewee, marching grid algorithm. [interview]. Dayton
Curry HB (1944) The method of steepest descent for non-linear minimizaton problems. Q Appl Math 2(3):258–261
Fletcher R, Reeves C (1964) Function minimization by conjugate gradients. Comput J 7(2):149–154
Kelley C (1999) Iterative methods for optimization, Society for Industrial and. Appl Math, Philadelphia
Fletcher R, Powell M (1963) A rapidly convergent descent method for optimization. Comput J 6(2):163–168
Nazareth L (1979) A relationship between the BFGS and conjugate gradient algorithms and its implications for new algorithms. SIAM J Numer Anal 16(5):794–800
Gen M, Cheng R (1997) Genetic algorithms and engineering design. Wiley, Hoboken
Eggleton RB, Guy RK (1988) Catalan strikes again! How likely is a function to be convex? Math Mag 61:211–219
Boyd S, Vandenberghe L (2004) Convex optimization. Cambridge University Press, Cambridge
Handleman P (2007) Air racing over Reno: the World's fastest motor sport. Specialty Press, Forest Lake
Reno Air Racing Association, “Reno Championship Air Races,” [Online]. Available: http://airrace.org/. Accessed 16 June 2016
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
French, M. (2018). Problems with More than One Variable. In: Fundamentals of Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-76192-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-76192-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76191-6
Online ISBN: 978-3-319-76192-3
eBook Packages: EngineeringEngineering (R0)