SIAM Journal on Optimization, Volume 31, Issue 2, Page 1352-1379, January 2021.
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic, and constraint function and derivative values can be computed explicitly, but the objective function is stochastic. It is assumed in this setting that it is intractable to compute objective function and derivative values explicitly, although one can compute stochastic function and gradient estimates. As a starting point for this stochastic setting, an algorithm is proposed for the deterministic setting that is modeled after a state-of-the-art line-search SQP algorithm but uses a stepsize selection scheme based on Lipschitz constants (or adaptively estimated Lipschitz constants) in place of the line search. This sets the stage for the proposed algorithm for the stochastic setting, for which it is assumed that line searches would be intractable. Under reasonable assumptions, convergence (resp., convergence in expectation) from remote starting points is proved for the proposed deterministic (resp., stochastic) algorithm. The results of numerical experiments demonstrate the practical performance of our proposed techniques.

中文翻译：

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非线性等式约束随机优化的序贯二次优化

SIAM优化杂志，第31卷，第2期，第1352-1379页，2021年1月。
提出了顺序二次优化算法来求解具有等式约束的光滑非线性优化问题。主要焦点是针对约束函数是确定性的情况，可以显式计算约束函数和导数，但目标函数是随机的情况下提出的算法。尽管可以计算随机函数和梯度估计值，但在这种情况下，假定显式计算目标函数和导数值是很困难的。作为此随机设置的起点，针对确定性设置，提出了一种算法，该算法以最新的线搜索SQP算法为模型，但是使用基于Lipschitz常数（或自适应估计的Lipschitz常数）的分步选择方案）代替行搜索。这为所提出的用于随机设置的算法设置了阶段，对于该算法，假定行搜索将是棘手的。在合理的假设下，对于所提出的确定性（随机性）算法，证明了从远程起点的收敛性（预期的收敛性）。数值实验的结果证明了我们提出的技术的实际性能。