Roma M., Pillo G. Large-Scale Nonlinear Optimization - Nonconvex Optimization and Its Applications

Springer Science+Business Media, Inc. -- 2006 -- ISBN13: 978-0387-30063-4This volume contains refereed papers presented at the Workshop on Large Scale Nonlinear Optimization held in Erice, Italy, at the "G. Stampacchia" International School of Mathematics of the "E. Majorana" Centre for Scientific Culture, during June 22-July 1,2004. The Workshop was the fourth in a series of Workshops on Nonlinear Optimization held in Erice; the three previous ones were held in 1995, 1998, 2001, respectively.
In the tradition of these meetings, the purpose of the Workshop was to review and discuss recent advances and promising research trends in the field of Nonlinear Optimization and its applications, with a main focus on the large dimensional case, currently at the forefront of the research effort.
The meeting was attended by 71 people from 18 different countries. Besides the lectures, several formal and informal discussions took place. The outcome was a wide and deep knowledge of the present research achievements and tendencies in the field. We wish to express our appreciation for the active contribution of all the participants in the meeting. By editing this volume we aim at enlarging the community of researchers, professionals and students who can benefit from this valuable knowledge.
The 16 papers included in this volume represent a significant selection of re- cent developments in Nonlinear Optimization theory and practice. They show that there are plenty of exciting ideas and new applications which give evi- dence of a fast evolution in the field. Moreover, they give an updated overview from different and complementary standpoints: theoretical analysis, algorith- mic development, implementation issues, real world applications.
In particular, as concerns unconstrained optimization, the paper by LukSan and VlEek is an up-to-date survey of efficient methods for large scale prob- lems, while Powell gives an accurate description of the derivative-free NEWUOA software. Large space in the volume is devoted to constrained optimization, from both a theoretical and algorithmic point of view. In fact, the paper by Bertsekas deals with sensitivity properties of Lagrange multipliers. Dostti reviews recently proposed algorithms for large quadratic programming prob-lems. Byrd et al., in their paper, give a detailed description of the KNITRO package for nonlinear programming. This package is designed for solving large scale problems; various algorithmic options, including two interior point meth- ods and an active-set method, are considered. A new class of preconditioners is proposed in the paper by Dollar et al.: implicit-factorization constraint preconditioners are considered for the iterative solution of symmetric linear systems arising from saddle-point problems. Preconditioning in one-step one-shot design optimization is considered in the paper by Griewank: in particular, the problem of minimizing an objective function subject to a very large dimen- sional state equation with a separate design space is tackled, addressing the issue of selecting a suitable preconditioner for the approximate reduced gradient. The use of exact penalty functions for solving generalized Nash equilib- rium problems is proposed by Facchinei and Pang; a broad algorithmic scheme for the solution of such problems is described too. In the paper by Mastroeni a variational model for traffic network problems is studied; in particular, the au- thor considers a generalized minimum cost flow problem formulated by means of a variational inequality. The paper by Bkrend et al, deals with the use of dedicated algebra solvers and an interior point algorithm for the efficient so- lution of the linear systems arising when solving an optimal control problem by a Runge-Kutta discretization scheme. Vector optimization is also treated: in the paper by Gutikrrez et al, approximate solutions of vector optimization problems are studied by means of a concept of approximate efficiency.
The paper by Evtushenko et al, deals with algorithms for constructing a family of parallel hyperplanes that separate two disjoint polyedra given by systems of linear inequalities; it is well known how the capability of finding such hyperplanes plays an important role in solving some practical problems. Another interesting problem is considered in the paper by Burdakov et al.: the problem, known as isotonic regression, has important applications in Opera- tions Research and Statistics, and it is often characterized by large dimension- ality. In order to solve such problems the authors introduce a new algorithm which exhibits both low computational complexity and high accuracy.
Finally, important real world applications are considered in the papers by Griesse and Volkwein, in the paper by Pesch et al. and in the paper by Peri et al. The first one considers boundary optimal control problems for a nonlinear reaction-diffusion equation system in three spatial dimensions. The second one presents a mathematical model for the dynamical behaviour of a molten carbonate fuel cell, which yields a large scale partial differential algebraic equation constrained optimization problem. The third one deals with optimum ship design problems and proposes the use of multi-objective formulations and global optimization strategies for their solution.