Nonlinear programming. Concepts, algorithms, and applications in chemical processes.

*(English)*Zbl 1207.90004This book is devoted to the presentation of nonlinear programming theory and algorithms concerning concepts, properties, problem formulations, optimality conditions as well as algorithms for solving unconstrained and constrained optimization problems, especially as they apply to challenging applications in chemical process engineering.

The book is divided into eleven chapters together with useful exercises at the end of each chapter. The author first presents the scope of optimization problems and an overview of nonlinear programming applications in process engineering. Concepts, properties and background for unconstrained multivariable nonlinear optimization, and derivative-free and gradient-based methods are given. Newton’s method for unconstrained optimization is presented. Note that in case second derivatives are not available, quasi-Newton methods can be applied. The author is concerned with the main concepts which characterize solutions of constrained optimization, and derives algorithms for equality constrained optimization. This approach is extended to nonlinear optimization problems involving equality and inequality constraints with algorithms which are incorporated into a wide variety of large-scale nonlinear programming solvers. The book addresses steady state process optimization and presents applications of nonlinear programming methods to modular and equation-oriented simulation environments. The author also deals with a general formulation for optimization with differential-algebraic equations and gives a survey of optimization strategies and current applications. He describes strategies for dynamic optimization in which he presents optimization methods with embedded differential-algebraic equation solvers and considers simultaneous collocation formulations for dynamic optimization problems and derives methods which embed discretized differential-algebraic equation models within the optimization formulation itself. Finally, the author presents complementarity models which can describe a class of discrete decisions, and describes a number of regularization and penalty formulations for mathematical programs with complementary constraints.

This is an interesting book on nonlinear programming. It is suitable for graduate and advanced undergraduate students in engineering, applied mathematics and operation research. It is a good reference for chemical engineers in using nonlinear programming algorithms and experts in optimization mathematics, researchers in process engineering and applied mathematics.

The book is divided into eleven chapters together with useful exercises at the end of each chapter. The author first presents the scope of optimization problems and an overview of nonlinear programming applications in process engineering. Concepts, properties and background for unconstrained multivariable nonlinear optimization, and derivative-free and gradient-based methods are given. Newton’s method for unconstrained optimization is presented. Note that in case second derivatives are not available, quasi-Newton methods can be applied. The author is concerned with the main concepts which characterize solutions of constrained optimization, and derives algorithms for equality constrained optimization. This approach is extended to nonlinear optimization problems involving equality and inequality constraints with algorithms which are incorporated into a wide variety of large-scale nonlinear programming solvers. The book addresses steady state process optimization and presents applications of nonlinear programming methods to modular and equation-oriented simulation environments. The author also deals with a general formulation for optimization with differential-algebraic equations and gives a survey of optimization strategies and current applications. He describes strategies for dynamic optimization in which he presents optimization methods with embedded differential-algebraic equation solvers and considers simultaneous collocation formulations for dynamic optimization problems and derives methods which embed discretized differential-algebraic equation models within the optimization formulation itself. Finally, the author presents complementarity models which can describe a class of discrete decisions, and describes a number of regularization and penalty formulations for mathematical programs with complementary constraints.

This is an interesting book on nonlinear programming. It is suitable for graduate and advanced undergraduate students in engineering, applied mathematics and operation research. It is a good reference for chemical engineers in using nonlinear programming algorithms and experts in optimization mathematics, researchers in process engineering and applied mathematics.

Reviewer: Do Van Luu (Hanoi)

##### MSC:

90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |

90C30 | Nonlinear programming |

90C90 | Applications of mathematical programming |

90C53 | Methods of quasi-Newton type |

90C56 | Derivative-free methods and methods using generalized derivatives |

90C46 | Optimality conditions and duality in mathematical programming |