\input zb-basic \input zb-matheduc \iteman{ZMATH 2015f.00969} \itemau{Guenin, Bertrand; K\"onemann, J.; Tun\c{c}el, L.} \itemti{A gentle introduction to optimization.} \itemso{Cambridge: Cambridge University Press (ISBN 978-1-107-65879-0/pbk; 978-1-107-05344-1/hbk). xi, 269~p. (2014).} \itemab This textbook will be the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. The chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives the readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material. One can get a very good idea of optimization problems all put in a practical context in Chapter 1. Chapter 2 deals with the solution of linear optimization problems. Chapter 3 discusses the linear programming duality through examples. The duality theory is developed in Chapter 4 and their application in Chapter 5. Chapter 6 is devoted to the solution of integer programs. Nonlinear optimization is treated in the last chapter, where optimality conditions are discussed and a brief overview of a primal-dual polynomial algorithms for linear programming based on ideas from nonlinear optimization is also given. \itemrv{Paulo Mbunga (Kiel)} \itemcc{N65 M45} \itemut{linear programs; integer programs; optimization problems on graphs; duality theory; branch and bound; nonlinear optimization; optimality conditions; nonconvex optimization problems; interior-point method; computational complexity} \itemli{} \end