10,234 research outputs found
Stochastic Trust Region Methods with Trust Region Radius Depending on Probabilistic Models
We present a stochastic trust-region model-based framework in which its
radius is related to the probabilistic models. Especially, we propose a
specific algorithm, termed STRME, in which the trust-region radius depends
linearly on the latest model gradient. The complexity of STRME method in
non-convex, convex and strongly convex settings has all been analyzed, which
matches the existing algorithms based on probabilistic properties. In addition,
several numerical experiments are carried out to reveal the benefits of the
proposed methods compared to the existing stochastic trust-region methods and
other relevant stochastic gradient methods
Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered
Efficient algorithms for the discovery of optimal control designs for
coherent control of quantum processes are of fundamental importance. One
important class of algorithms are sequential update algorithms generally
attributed to Krotov. Although widely and often successfully used, the
associated theory is often involved and leaves many crucial questions
unanswered, from the monotonicity and convergence of the algorithm to
discretization effects, leading to the introduction of ad-hoc penalty terms and
suboptimal update schemes detrimental to the performance of the algorithm. We
present a general framework for sequential update algorithms including specific
prescriptions for efficient update rules with inexpensive dynamic search length
control, taking into account discretization effects and eliminating the need
for ad-hoc penalty terms. The latter, while necessary to regularize the problem
in the limit of infinite time resolution, i.e., the continuum limit, are shown
to be undesirable and unnecessary in the practically relevant case of finite
time resolution. Numerical examples show that the ideas underlying many of
these results extend even beyond what can be rigorously proved.Comment: 19 pages, many figure
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