A scalable sequential adaptive cubic regularization algorithm for optimization with general equality constraints

doi:10.1007/s11075-026-02401-z

A scalable sequential adaptive cubic regularization algorithm for optimization with general equality constraints

2026-05-01

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Maurício Silva Louzeiro

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Detong Zhu

DOI：10.1007/s11075-026-02401-z

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The scalable adaptive cubic regularization method (ARC(q)K: [1]) has been recently proposed for unconstrained optimization. It has excellent convergence properties, well-defined complexity bounds, and promising numerical performance. In this paper, we extend ARC(q)K to nonlinear optimization with general equality constraints and propose a scalable sequential adaptive cubic regularization algorithm named SSARC(q)K. In each iteration, we construct an ARC subproblem with linearized constraints inspired by sequential quadratic optimization methods. Next, a composite-step approach is used to decompose the trial step into the sum of a vertical step and a horizontal step. By means of the reduced-Hessian approach, we rewrite the linearly constrained ARC subproblem as a standard unconstrained ARC subproblem to compute the horizontal step. Analogous to ARC(q)K, we employ a CG-Lanczos procedure with shifts to solve ARC subproblems inexactly, thus bypassing any hard case consideration. This also avoids solving the subproblem multiple times for obtaining a new iterative point. We establish the global convergence of the inexact ARC method SSARC(q)K to first-order critical points. Preliminary numerical tests and some comparison results are presented to illustrate the performance of SSARC(q)K.

Keywords:

Nonlinear constrained optimization

Adaptive regularization with cubics

Global convergence

A scalable sequential adaptive cubic regularization algorithm for optimization with general equality constraints

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