Nonlinear Programming: Theory and Algorithms

Review of the book
Nonlinear programming is related to problems in which the constraints or the objective function are not linear. One of the methods used in operations research to solve nonlinear models is to approximate the nonlinear relationships linearly and then solve them using linear programming methods. But some problems cannot be linearized and must be solved non-linearly. Solving such models has received much attention in the last 4 decades.

Table of Contents
The content presented in this book is as follows:

1- Introduction to nonlinear programming
2- Convex sets
3- Convex functions
4- Optimality conditions of KKT and Fritz John
5- Lagrangian relaxation and duality theory
6- The idea of non-linear algorithms
7- Unconstraint optimization
8- Penalty and barrier functions
9- Possible direction method
10- linear complementary problem, fractional, geometric and quadratic programming
11- An overview of linear programming
12- An overview of convexity, optimality conditions and duality theory