DUALITY RELATIONSHIPS FOR ENTROPY-LIKE MINIMIZATION PROBLEMS
DUALITY RELATIONSHIPS FOR ENTROPY-LIKE MINIMIZATION PROBLEMS
复制标题
DOI：
10.1137/0329017
复制
发表时间：
1991-03-01
影响因子：
2.2
通讯作者：
LEWIS, AS
中科院分区：
文献类型：
--
作者：
BORWEIN, JM;LEWIS, AS
本文考虑在有限数量的线性等式约束下，L(p) 空间的正圆锥上的凸积分函数的最小化。 此类问题出现在谱估计中，其中目标函数通常是类熵的，并且是受约束的近似。 拉格朗日对偶问题是有限维且无约束的。 在准内部约束条件下，原值和对偶值相等，具有对偶成就。 示例表明可能无法达到原始值。 给出的条件确保可以直接从对偶最优解计算出原始最优解。 在许多示例中都满足这些条件。
This paper considers the minimization of a convex integral functional over the positive cone of an L(p) space, subject to a finite number of linear equality constraints. Such problems arise in spectral estimation, where the objective function is often entropy-like, and in constrained approximation. The Lagrangian dual problem is finite-dimensional and unconstrained. Under a quasi-interior constraint qualification, the primal and dual values are equal, with dual attainment. Examples show the primal value may not be attained. Conditions are given that ensure that the primal optimal solution can be calculated directly from a dual optimum. These conditions are satisfied in many examples.