Multilevel decision theory arises to resolve the contradiction between increasing requirements towards the process of design, synthesis, control and management of complex systems and the limitation of the power of technical, control, computer and other executive devices, which have to perform actions and to satisfy requirements in real time. This theory rises suggestions how to replace the centralised management of the system by hierarchical co-ordination of sub-processes. All sub-processes have lower dimensions, which support easier management and decision making. But the sub-processes are...

Techniques and principles of minimax theory play a key role in many areas of research, including game theory, optimization, and computational complexity. In general, a minimax problem can be formulated as min max f(x, y) (1),"EX lEY where f(x, y) is a function defined on the product of X and Y spaces. There are two basic issues regarding minimax problems: The first issue concerns the establishment of sufficient and necessary conditions for equality minmaxf(x, y) = maxminf(x, y). (2) "'EX lEY lEY "'EX The classical minimax theorem of von Neumann is a result of this type. Duality theory in...

2. The Algorithm ...59 3. Convergence Analysis ..., ...60 4. Complexity Analysis ...63 5. Conclusions ...67 References ...67 A Simple Proof for a Result of Ollerenshaw on Steiner Trees ...68 Xiufeng Du, Ding-Zhu Du, Biao Gao, and Lixue Qii 1. Introduction ...68 2. In the Euclidean Plane ...69 3. In the Rectilinear Plane ...70 4. Discussion ...-...71 References ...71 Optimization Algorithms for the Satisfiability (SAT) Problem ...72 Jun Gu 1. Introduction ...72 2. A Classification of SAT Algorithms ...7:3 3. Preliminaries ...IV 4. Complete Algorithms and Incomplete Algorithms ...81 5....

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and...

Semi-infinite optimization is a vivid field of active research. Recently semi- infinite optimization in a general form has attracted a lot of attention, not only because of its surprising structural aspects, but also due to the large number of applications which can be formulated as general semi-infinite programs. The aim of this book is to highlight structural aspects of general semi-infinite programming, to formulate optimality conditions which take this structure into account, and to give a conceptually new solution method. In fact, under certain assumptions general semi-infinite programs...

For both public and private managers, the book Optimization Methods for a Stakeholder Society is today's key to answer the problem of a sustainable development world. This world has to take into account the meaning of all stakeholders involved and has to reconcile a number of objectives, such as economic growth, employment and preservation of the ecosystem. Traditional methods, such as cost-benefit, are outmoded as they translate all these objectives into monetary costs, a materialistic approach. On the contrary, objectives have rather to stick to their own units, eventually...

The field of global optimization has been developing at a rapid pace. There is a journal devoted to the topic, as well as many publications and notable books discussing various aspects of global optimization. This book is intended to complement these other publications with a focus on stochastic methods for global optimization. Stochastic methods, such as simulated annealing and genetic algo- rithms, are gaining in popularity among practitioners and engineers be- they are relatively easy to program on a computer and may be cause applied to a broad class of global optimization problems....

Boundary value problems which have variational expressions in form of inequal- ities can be divided into two main classes. The class of boundary value prob- lems (BVPs) leading to variational inequalities and the class of BVPs leading to hemivariational inequalities. The first class is related to convex energy functions and has being studied over the last forty years and the second class is related to nonconvex energy functions and has a shorter research "life" beginning with the works of the second author of the present book in the year 1981. Nevertheless a variety of important results have...

Global optimization is one of the fastest developing fields in mathematical optimization. In fact, an increasing number of remarkably efficient deterministic algorithms have been proposed in the last ten years for solving several classes of large scale specially structured problems encountered in such areas as chemical engineering, financial engineering, location and network optimization, production and inventory control, engineering design, computational geometry, and multi-objective and multi-level optimization.
These new developments motivated the authors to write a new book devoted...

Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models. There are several arenas model is appropriate, and such models have found applications in air- line yield management, capacity planning, electric power generation planning, financial planning, logistics, telecommunications network planning, and many more. In some of these applications, modelers represent uncertainty in terms of only a few seenarios and formulate a large scale linear program which is then solved...