偶也没有用过这种方法，你用google搜一下，其中偶搜的一个解释，这个算法介绍的也不多，而且有局限性，你看看下面的说明好了。
Interior-point solvers for nonlinear programming are the subjects of intense current investigation. An algorithm of this class, known as the sequential unconstrained minimization technique (SUMT) was actually proposed in the 1960s, in the book of Fiacco and McCormick (1968). The idea at that time was to define a barrier-penalty function for the NLP as follows:
where is a small positive parameter. Given some value of , the algorithm finds an approximation to the minimizer of . It then decreases and repeats the minimization process. Under certain assumptions, one can show that as so the sequence of iterates generated by SUMT should approach the solution of the nonlinear program provided that is decreased to zero. The difficulties with this approach are that all iterates must remain strictly feasible with respect to the inequality constraints (otherwise the log functions are not defined), and the subproblem of minimizing becomes increasingly difficult to solve as becomes small, as the Hessian of this function becomes highly ill conditioned and the radius of convergence becomes tiny. Many implementations of this approach were attempted, including some with enhancements such as extrapolation to obtain good starting points for each value of . However, the approach does not survive in the present generation of software, except through its profound influence on the interior-point research of the past 15 years.
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发表于 2003-8-15 20:28:59
发表于 2003-8-15 22:26:09
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