英和和英

出典:『Wikipedia』 (2011/06/17 22:17 UTC 版)

英語による解説

引用

In constrained optimization, it is often possible to convert the primal problem (i.e. the original form of the optimization problem) to a dual form, which is termed a dual problem. Usually "dual problem" refers to the "Lagrangian dual problem" but other dual problems are used, for example, the Wolfe dual problem and the Fenchel dual problem. The Lagrangian dual problem is obtained by forming the Lagrangian, using nonnegative Lagrangian multipliers to add the constraints to the objective function, and then solving for some primal variable values that minimize the Lagrangian. This solution gives the primal variables as functions of the Lagrange multipliers, which are called dual variables, so that the new problem is to maximize the objective function with respect to the dual variables under the derived constraints on the dual variables (including at least the nonnegativity).