It is known that the vip can be reformulated as an unconstrained minimization problem through the d - gap function 我們知道,通過廣義d -間隙函數,可以將變分不等式問題轉化為一個無約束極小化問題。
We constitute the corresponding derivative - free descent algorithm . after we proved the well - definition and global convergence of our derivative - free descent algorithm , we compare our algorithm with some existent derivative - free descent algorithms based on unconstrained minimization formulation 在證明了所構造的derivative - free算法的合理性以及整體收斂性之后,我們將所構造的算法與以前已經存在的無約束型的derivative - free算法進行了比較。
Chapter 4 studies the techniques for numerical realization of the dual algorithms and generalization of the dual algorithms to general unconstrained nonlinear programming . at first , we construct modified dual algorithms to overcome the drawback that it needs to resolve a sequential unconstrained minimization problems exactly in the step 2 of the dual algorithms in chapter 2 and chapter 3 首先針對前兩章的對偶算法由于需要精確求解一系列無約束極小化問題,因而實際計算中很難實現這一缺點,構造修正的對偶算法,即,關于勢函數的無約束極小化問題無需精確求解的對偶算法。
By intro - ducing a penalty function as the following , for every e > 0 , we construct a sequence of unconstrained minimization problems to approximate the constrained minimization problem . the solutions of such a sequence of unconstrained minimization problems all exist , and they converge to the solution of the constrained minimization problem in a certain sense 這列無約束極小化問題( p _ )的解都是存在的,并且在某種意義下收斂至原始約束極小化問題( p )的解,不僅如此,它們的性能指標也收斂至原始問題( p )解的性能指標。