Theory of Global Random Search [Paperback]

1 Global Optimization: An Overview.- 1. Global Optimization Theory: General Concepts.- 1.1. Statements of the global optimization problem.- 1.2. Types of prior information about the objective function and a classification of methods.- 1.2.1. Types of prior information.- 1.2.2. Classification of principal approaches and methods of the global optimization.- 1.2.3. General properties of multiextremal functions.- 1.3. Comparison and practical use of global optimization algorithms.- 1.3.1. Numerical comparison.- 1.3.2. Theoretical comparison criteria.- 1.3.3. Practical optimization problems.- 2. Global Optimization Methods.- 2.1. Global optimization algorithms based on the use of local search techniques.- 2.1.1. Local optimization algorithms.- 2.1.2. Use of local algorithms in constructing global optimization strategies.- 2.1.3. Multistart.- 2.1.4. Tunneling algorithms.- 2.1.5. Methods of transition from one local minimizer into another.- 2.1.6. Algorithms based on smoothing the objective function.- 2.2. Set covering methods.- 2.2.1. Grid algorithms (Passive coverings).- 2.2.2. Sequential covering methods.- 2.2.3. Optimality of global minimization algorithms.- 2.3. One-dimensional optimization, reduction and partition techniques.- 2.3.1. One-dimensional global optimization.- 2.3.2. Dimension reduction in multiextremal problems.- 2.3.3. Reducing global optimization to other problems in computational mathematics.- 2.3.4. Branch and bound methods.- 2.4. An approach based on stochastic and axiomatic models of the objective function.- 2.4.1. Stochastic models.- 2.4.2. Global optimization methods based on stochastic models.- 2.4.3. The Wiener process case.- 2.4.4. Axiomatic approach.- 2.4.5. Information-statistical approach.- 2. Global Random Search.- 3. Main Concepts and Approaches of Global Random Search.- 3.1. Construction of global random search algorithms: Basic approaches.- 3.1.1. Uniform random sampling.- 3.1.2. General (nonuniform) random sampling.- 3.1.3. Ways of imprls(