In this introduction we give an overview of mathematical optimization, focusing on the special role of convex optimization. The concepts introduced informally here will be covered in later chapters, with more care and technical detail.
1.1 Mathematical optimization
A mathematical optimization problem, or just optimization problem, has the form
Here the vector x = (x1, . . . , xn) is the optimization variable of the problem, the function f0 : Rn → R is the objective function, the functions fi : Rn → R, i = 1, . . . , m, are the (inequality) constraint functions, and the constants b1, . . . , bm are the limits, ...