A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear-Equality-Constrained Optimization with Rank-Deficient Jacobians

Albert S. Berahas (), Frank E. Curtis (), Michael J. O’Neill () and Daniel P. Robinson ()
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Albert S. Berahas: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109
Frank E. Curtis: Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015
Michael J. O’Neill: Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599
Daniel P. Robinson: Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, Pennsylvania 18015

Mathematics of Operations Research, 2024, vol. 49, issue 4, 2212-2248

Abstract: 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. 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 with popular alternatives.

Keywords: 49M05; 49M10; 49M37; 65K05; 65K10; 90C15; 90C30; 90C55; nonlinear optimization; stochastic optimization; stochastic average approximation; sequential quadratic optimization; rank deficiency (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:4:p:2212-2248

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