A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems

• URL: http://arxiv.org/abs/2304.14907v3
• Date: Wed, 13 Mar 2024 18:34:31 GMT
• Title: A Stochastic-Gradient-based Interior-Point Algorithm for Solving Smooth Bound-Constrained Optimization Problems
• Authors: Frank E. Curtis, Vyacheslav Kungurtsev, Daniel P. Robinson, Qi Wang,
• Abstract summary: The proposed algorithm is based on the subject-point unique constraints from other interior-point methods. It is shown that with a careful balance between the projection, step-size and sequence sequences, the proposed algorithm convergence guarantees in both numerical and deterministic settings.
• Score: 12.29270365918848
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results. The algorithm is unique from other interior-point methods for solving smooth nonconvex optimization problems since the search directions are computed using stochastic gradient estimates. It is also unique in its use of inner neighborhoods of the feasible region -- defined by a positive and vanishing neighborhood-parameter sequence -- in which the iterates are forced to remain. It is shown that with a careful balance between the barrier, step-size, and neighborhood sequences, the proposed algorithm satisfies convergence guarantees in both deterministic and stochastic settings. The results of numerical experiments show that in both settings the algorithm can outperform projection-based methods.

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