Sequential unconstrained minimization algorithms for constrained optimization
Sequential unconstrained minimization algorithms for constrained optimization
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DOI：
10.1088/0266-5611/24/1/015013
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发表时间：
2008-02-01
期刊：
影响因子：
2.1
通讯作者：
Byrne, Charles
中科院分区：
文献类型：
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作者：
Byrne, Charles
受向量变量x约束的函数f(X)：R(J)->；R的极小化问题经常出现在反问题中。即使在没有约束的情况下，寻找f(X)的最小值也可能需要迭代方法。在这里，我们考虑了一类一般的迭代算法，它们将约束极小化问题的解作为一个向量序列的极限，每个迭代算法求解一个无约束极小化问题。我们的序列无约束最小化算法(SUMMA)是一个求解约束最小化的迭代过程。在第k步，我们最小化函数G(K)(X)=f(X)+g(K)(X)，以得到x(K)。R(J)->；R(+)的辅助函数g(K)(X)：D的子集在集合D上是非负的，每个xk都设在D内，目标是最小化集合C=(D)上的连续函数f：R(J)->；R(+)。我们假设函数g(K)(X)满足不等式0
The problem of minimizing a function f ( x) : R(J) -> R, subject to constraints on the vector variable x, occurs frequently in inverse problems. Even without constraints, finding a minimizer of f ( x) may require iterative methods. We consider here a general class of iterative algorithms that find a solution to the constrained minimization problem as the limit of a sequence of vectors, each solving an unconstrained minimization problem. Our sequential unconstrained minimization algorithm ( SUMMA) is an iterative procedure for constrained minimization. At the kth step we minimize the functionG(k)( x) = f ( x) + g(k)( x),to obtain x(k). The auxiliary functions g(k)( x) : D subset of R(J) -> R(+) are nonnegative on the set D, each xk is assumed to lie within D, and the objective is to minimize the continuous function f : R(J) -> R over x in the set C = (D) over bar, the closure of D. We assume that such minimizers exist, and denote one such by (x) over cap. We assume that the functions g(k)(x) satisfy the inequalities0