Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 168', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 10. Minimization or Maximization of Functions Introduction In a nutshell You are given a single function f that depends on one or more independent variables. You want to find the value of those variables where f takes on a maximum or a minimum value. You can then calculate what value of f is achieved at the maximum or minimum. The tasks of maximization and minimization are trivially related to each other since one person s function f could just as well be another s -f. The computational desiderata are the usual ones Do it quickly cheaply and in small memory. Often the computational effort is dominated by the cost of evaluating f and also perhaps its partial derivatives with respect to all variables if the chosen algorithm requires them . In such cases the desiderata are sometimes replaced by the simple surrogate Evaluate f as few times as possible. An extremum maximum or minimum point can be either global truly the highest or lowest function value or local the highest or lowest in a finite neighborhood and not on the boundary of that neighborhood . See Figure . Finding a global extremum is in general a very difficult problem. Two standard heuristics are widely used i find local extrema starting from widely varying starting values of the independent variables perhaps chosen quasi-randomly as in and then pick the most extreme of these if they are not all the same or ii perturb a local extremum by taking a finite amplitude step away from it and then see if your routine returns you to a better point or always to the same one. Relatively recently so-called simulated annealing methods have demonstrated important successes on a variety of global extremization problems. Our chapter title could just as well be optimization which is the usual name for this very large field of numerical research. The importance ascribed to the various tasks in this field depends strongly on the particular interests of whom you talk to. Economists and some engineers
