A Projective Sequential Adaptive Cubic Regularisation Algorithm for Constrained Optimization

doi:10.1007/s10255-025-0084-8

A Projective Sequential Adaptive Cubic Regularisation Algorithm for Constrained Optimization

2025-12-01

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DOI：10.1007/s10255-025-0084-8

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A projective sequential adaptive regularization algorithm using cubics (ARC) with line search filter techniques is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic optimization methods. In each iteration, a constrained ARC subproblem is constructed to generate a new step. By using composite step approaches and a projective matrix, we transform the constrained ARC subproblem into a standard unconstrained ARC subproblem. After the new step is computed, we employ line search filter techniques to generate the next iteration point. Global convergence is analyzed under some mild assumptions. Preliminary numerical results are reported.

Keywords:

nonlinear optimization

cubic regularization

global convergence

line search filter

sequential quadratic optimization

A Projective Sequential Adaptive Cubic Regularisation Algorithm for Constrained Optimization

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