Optimization: Algorithms and Applications

Optimization: Algorithms and Applications presents a variety of techniques for optimization problems, and it emphasizes concepts rather than the mathematical details and proofs.

The book illustrates how to use gradient and stochastic methods for solving unconstrained and constrained optimization problems. It discusses the conjugate gradient method, the Broyden–Fletcher–Goldfarb–Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible directions, genetic algorithms, particle swarm optimization (PSO), simulated annealing, ant colony optimization, and tabu search methods. The author shows how to solve nonconvex multi-objective optimization problems using simple modifications of the basic PSO code. The book also introduces multidisciplinary design optimization (MDO) architectures, and develops software codes for the simplex method and affine-scaling interior point method for solving linear programming problems. In addition, it examines Gomory’s cutting plane method, the branch-and-bound method, and Balas’ algorithm for integer programming problems.

The author follows a step-by-step approach to developing the MATLAB codes from the algorithms. He then applies the codes to solve both standard functions taken from the literature and real-world applications, including a complex trajectory design problem of a robot, a portfolio optimization problem, and a multi-objective shape optimization problem of a reentry body. This hands-on approach improves  understanding and confidence in handling different solution methods. 

The MATLAB codes are available on the book’s CRC Press web page.