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Stochastic Global Optimization Methods and Applications to Chemical, Biochemical, Pharmaceutical and Environmental Processes
1 online resource (312 pages) : illustrations
Front Cover; Stochastic Global Optimization Methods and Applications to Chemical, Biochemical, Pharmaceutical and Environmental Processes; Stochastic Global Optimization Methods and Applications to Chemical, Biochemical, Pharmaceutical and Environmental Processe ... ; Copyright; Contents; About the authors; Preface; 1 -- Basic features and concepts of optimization; 1.1 Introduction; 1.2 Basic features; 1.2.1 Optimization and its benefits; 1.2.2 Scope for optimization; 1.2.3 Illustrative examples; 1.2.4 Essential requisites for optimization; 1.3 Basic concepts; 1.3.1 Functions in optimization
1.3.2 Interpretation of behavior of functions1.3.3 Maxima and minima of functions; 1.3.4 Region of search for constrained optimization; 1.4 Classification and general procedure; 1.4.1 Classification of optimization problems; 1.4.2 General procedure of solving optimization problems; 1.4.3 Bottlenecks in optimization; 1.5 Summary; References; 2 -- Classical analytical methods of optimization; 2.1 Introduction; 2.2 Statement of optimization problem; 2.3 Analytical methods for unconstrained single-variable functions; 2.3.1 Necessary and sufficient conditions
2.3.2 Sufficient conditions for convexity and concavity of a function2.4 Analytical methods for unconstrained multivariable functions; 2.4.1 Necessary and sufficient conditions; 2.4.2 Two-variable function; 2.4.3 Multivariable function; 2.5 Analytical methods for multivariable optimization problems with equality constraints; 2.5.1 Direct substitution; 2.5.2 Penalty function approach; 2.5.3 Method of Lagrange multipliers; 2.5.3.1 Necessary condition for a basic problem; 2.5.3.2 Necessary condition for a general problem; 2.5.3.3 Sufficient conditions for a general problem
2.6 Analytical methods for solving multivariable optimization problems with inequality constraints2.6.1 Kuhn-Tucker conditions for problems with inequality constraints; 2.6.2 Kuhn-Tucker conditions for problems with inequality and equality constraints; 2.7 Limitations of classical optimization methods; 2.8 Summary; References; 3 -- Numerical search methods for unconstrained optimization problems; 3.1 Introduction; 3.2 Classification of numerical search methods; 3.2.1 Direct search methods; 3.2.2 Gradient search methods; 3.3 One-dimensional gradient search methods; 3.3.1 Newton's method
3.3.2 Quasi-Newton method3.3.3 Secant method; 3.4 Polynomial approximation methods; 3.4.1 Quadratic interpolation method; 3.4.2 Cubic interpolation method; 3.5 Multivariable direct search methods; 3.5.1 Univariate search method; 3.5.2 Hooke-Jeeves pattern search method; 3.5.2.1 Exploratory move; 3.5.2.2 Pattern move; 3.5.3 Powell's conjugate direction method; 3.5.4 Nelder-Mead simplex method; 3.6 Multivariable gradient search methods; 3.6.1 Steepest descent method; 3.6.2 Multivariable Newton's method; 3.6.3 Conjugate gradient method; 3.7 Summary; References
4 -- Stochastic and evolutionary optimization algorithms
Ch. Venkateswarlu, Satya Eswari Jujjavarapu.
Includes bibliographical references and index.