Worst-case complexity of an SQP method for nonlinear equality constrained stochastic optimization
Worst-case complexity of an SQP method for nonlinear equality constrained stochastic optimization
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DOI：
10.1007/s10107-023-01981-1
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
Frank E. Curtis;Michael O'Neill;Daniel P. Robinson
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文献类型：
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作者：
Frank E. Curtis;Michael O'Neill;Daniel P. Robinson
一个最坏情况下的复杂性界证明了序列二次优化（通常称为SQP）算法，已被设计用于解决涉及随机目标函数和确定性非线性等式约束的优化问题。除了由于单调非递增的价值参数序列的自适应性而产生的附加项之外，证明的复杂性界与无约束非凸优化的随机梯度算法的复杂性界相当。的整体复杂性的界限，这占了适应性的优点参数序列，表明结果相比，无约束的设置（与额外的对数因子）持有高概率。
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear equality constraints. Barring additional terms that arise due to the adaptivity of the monotonically nonincreasing merit parameter sequence, the proved complexity bound is comparable to that known for the stochastic gradient algorithm for unconstrained nonconvex optimization. The overall complexity bound, which accounts for the adaptivity of the merit parameter sequence, shows that a result comparable to the unconstrained setting (with additional logarithmic factors) holds with high probability.