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Penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem. The unconstrained problems are formed by adding a term, called a penalty function, to the objective function that consists of a ''penalty parameter'' multiplied by a measure of violation of the constraints. The measure of violation is nonzero when the constraints are violated and is zero in the region where constraints are not violated. == Example == Let us say we are solving the following constrained problem: : subject to : This problem can be solved as a series of unconstrained minimization problems : where : In the above equations, is the ''penalty function'' while are the ''penalty coefficients''. In each iteration ''k'' of the method, we increase the penalty coefficient (e.g. by a factor of 10), solve the unconstrained problem and use the solution as the initial guess for the next iteration. Solutions of the successive unconstrained problems will eventually converge to the solution of the original constrained problem. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「penalty method」の詳細全文を読む スポンサード リンク
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