On the Relation between Stochastic and Deterministic Optimization
On the Relation between Stochastic and Deterministic Optimization
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论随机优化与确定性优化的关系
DOI：
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发表时间：
1975
期刊：
影响因子：
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通讯作者：
R. Wets
中科院分区：
文献类型：
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作者：
R. Wets
结果表明，在控制策略的选择具有非预期性约束的情况下，随机优化问题与确定性优化问题是等价的。该条件可以以约束的形式显式地引入。这样做，导致一个优化问题，它是可能的，以获得最优性标准。这里考虑凸的情况。它表明，与非预期性限制的变量形成一个鞅。这些变量可以用来制定一个等价的问题，允许逐点优化，结果强烈类似于最大值原理。最后用两个简单的例子来说明主要结果。
It is shown that stochastic optimization problems ressemble deterministic optimization problems up to the nonanticipativity restriction on the choice of the control policy. This condition can be introduced explicitly in the form of a constraint. Doing so, lead to an optimization problem for which it is possible to derive optimality criteria. The convex case is considered here. It is shown that the variables associated with the nonanticipativity restriction form a martingale. These variables can be used to formulate an equivalent problem allowing for pointwise optimization, a result strongly akin to the Maximum principle. Finally two simple examples are used to illustrate the main results.