A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear Equality Constrained Optimization with Rank-Deficient Jacobians
This work addresses optimization problems with stochasticity and rank-deficient constraints, which is incremental as it builds on existing step decomposition strategies.
The authors tackled nonlinear equality constrained optimization with stochastic objectives and rank-deficient Jacobians by proposing a sequential quadratic optimization algorithm that uses stochastic gradient estimates and ensures convergence, demonstrating superior performance compared to popular alternatives in numerical experiments.
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic structure of the proposed method is based on a step decomposition strategy that is known in the literature to be widely effective in practice, wherein each search direction is computed as the sum of a normal step (toward linearized feasibility) and a tangential step (toward objective decrease in the null space of the constraint Jacobian). However, the proposed method is unique from others in the literature in that it both allows the use of stochastic objective gradient estimates and possesses convergence guarantees even in the setting in which the constraint Jacobians may be rank deficient. The results of numerical experiments demonstrate that the algorithm offers superior performance when compared to popular alternatives.