What is it about?
This is well-written introduction to the simpler techniques of optimization---for example, linear and integer programming re given an airing but not dynamic programming---for suitable for those reading pure mathematics as a specialist subject in their first year of undergraduate studies. Although the authors of the book have in mind undergraduates in other subjects (such as operational research and economics) who are reading pure mathematics as a subsidiary subject, such readers would probably need go have at least two years background in pure mathematics. The reviewer (an economist, not a mathematician) found it somewhat bizarre that a book mostly suitable for students mathematicians should deal (rather lightly) with convex sets--for example, there is no proof of the (full) Minkowski- Farkas theorem on separating hyperplanes--- and even then these sets are treated a f t e r consideration of linear programming. However, the other gripes that the reviewer has are very small in number and minor in nature.
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Perspectives
As regards the application of optimisation techniques in economics, it should be pointed out that such techniques (and the oft-associated concept of equilibirum )are almost wholly confined to mainstream (viz. neoclassical) economics, the school of economic thinking that has provided the theoretical basis of much policy-advice to Western governments . . . and created the economic mess in which over half the World finds itself. Other schools of economic thinking eschew the concept of equilibrium and emphasize uncertainty (which is quite distinct from risk); where these schools alternative to the neoclassical one employ mathematics, it would be the mathematics iof non-linear and chaotic systems that would be much more appropriate the mathematics of linear systems.
Paul Hudson
Read the Original
This page is a summary of: A gentle guide to optimization by B. Guenin, J. Könemann and L. Tunçel, pp 269, £59.99 (paper), ISBN: 978-107-65879-0, Cambridge University Press (2014)., The Mathematical Gazette, June 2016, Cambridge University Press,
DOI: 10.1017/mag.2016.93.
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