Handbook of test problems in local and global optimization.

*(English)*Zbl 0943.90001
Nonconvex Optimization and Its Applications. 33. Dordrecht: Kluwer Academic Publishers. xv, 441 p. (1999).

The book presents a collection of test problems for mathematical optimization, where the following categories are covered: Quadratic programming problems (10), quadratically constrained problems (4), univariate polynomial problems (9), bilinear problems (8), biconvex and difference of convex function problems (14), generalized geometric programming (16), twice continuously differentiable NLPs (46), bilevel programming problems (19), complementary problems (12), semidefinite programming problems (1), mixed-integer nonlinear problems (12), combinatorial optimization problems (10), nonlinear systems of equations (18), dynamic optimization problems (25).

The number of test examples that can be downloaded from the home page of the first author, is shown in brackets. The codes are available either in the GAMS or in case of dynamic optimization, the MINOPT format, a modeling language developed at the same institute. Moreover, the book contains numerous links to existing test problem collections related to the topics.

The purpose of the book is to present a large collection of mathematical optimization problems where most of them model a practical application, in particular from computational chemistry. The mathematical structure of the optimization problem, and a brief outline of the underlying model type are presented, also a review on available solution methods.

The test problem collection might be useful for people developing optimization software, and for those who would like to get a review about various classes of mathematical optimization problems that can be solved in practice. Moreover, it is certainly valuable also for chemical engineers who want to become familiar with mathematical modeling.

Main emphasis is to find a global solution in case of a nonconvex NLP, not a local one. Links or references to some standard test problems collections and test problem generators are missing, e.g., to the widely used CUTE test problem collection.

The number of test examples that can be downloaded from the home page of the first author, is shown in brackets. The codes are available either in the GAMS or in case of dynamic optimization, the MINOPT format, a modeling language developed at the same institute. Moreover, the book contains numerous links to existing test problem collections related to the topics.

The purpose of the book is to present a large collection of mathematical optimization problems where most of them model a practical application, in particular from computational chemistry. The mathematical structure of the optimization problem, and a brief outline of the underlying model type are presented, also a review on available solution methods.

The test problem collection might be useful for people developing optimization software, and for those who would like to get a review about various classes of mathematical optimization problems that can be solved in practice. Moreover, it is certainly valuable also for chemical engineers who want to become familiar with mathematical modeling.

Main emphasis is to find a global solution in case of a nonconvex NLP, not a local one. Links or references to some standard test problems collections and test problem generators are missing, e.g., to the widely used CUTE test problem collection.

Reviewer: Klaus Schittkowski (Bayreuth)

##### MSC:

90-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to operations research and mathematical programming |

90-08 | Computational methods for problems pertaining to operations research and mathematical programming |

90Cxx | Mathematical programming |