A Sequential Quadratic Programming Method with High Probability Complexity Bounds for Nonlinear Equality Constrained Stochastic Optimization

• URL: http://arxiv.org/abs/2301.00477v1
• Date: Sun, 1 Jan 2023 21:46:50 GMT
• Title: A Sequential Quadratic Programming Method with High Probability Complexity Bounds for Nonlinear Equality Constrained Stochastic Optimization
• Authors: Albert S. Berahas, Miaolan Xie and Baoyu Zhou
• Abstract summary: It is assumed that constraint function values and derivatives are available, but only programming approximations of the objective function and its associated derivatives can be computed. A high-probability bound on the iteration complexity of the algorithm to approximate first-order stationarity is derived.
• Score: 2.535271349350579
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic approximations of the objective function and its associated derivatives can be computed via inexact probabilistic zeroth- and first-order oracles. Under reasonable assumptions, a high-probability bound on the iteration complexity of the algorithm to approximate first-order stationarity is derived. Numerical results on standard nonlinear optimization test problems illustrate the advantages and limitations of our proposed method.

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