An objective-function-free algorithm for nonconvex stochastic optimization with deterministic equality and inequality constraints
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917374704222208 |
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| author | Gratton, S. Toint, Ph. L. |
| author_facet | Gratton, S. Toint, Ph. L. |
| contents | An algorithm is proposed for solving optimization problems with stochastic objective and deterministic equality and inequality constraints. This algorithm is objective-function-free in the sense that it only uses the objective's gradient and never evaluates the function value. It is based on an adaptive selection of function-decreasing and constraint-improving iterations, the first ones using an Adagrad-type stepsize. When applied to problems with full-rank Jacobian, the combined primal-dual optimality measure is shown to decrease at the rate of O(1/sqrt{k}), which is identical to the convergence rate of first-order methods in the unconstrained case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29685 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An objective-function-free algorithm for nonconvex stochastic optimization with deterministic equality and inequality constraints Gratton, S. Toint, Ph. L. Optimization and Control 49M37, 65K05, 65Y20 F.2.1; G.1.6 An algorithm is proposed for solving optimization problems with stochastic objective and deterministic equality and inequality constraints. This algorithm is objective-function-free in the sense that it only uses the objective's gradient and never evaluates the function value. It is based on an adaptive selection of function-decreasing and constraint-improving iterations, the first ones using an Adagrad-type stepsize. When applied to problems with full-rank Jacobian, the combined primal-dual optimality measure is shown to decrease at the rate of O(1/sqrt{k}), which is identical to the convergence rate of first-order methods in the unconstrained case. |
| title | An objective-function-free algorithm for nonconvex stochastic optimization with deterministic equality and inequality constraints |
| topic | Optimization and Control 49M37, 65K05, 65Y20 F.2.1; G.1.6 |
| url | https://arxiv.org/abs/2603.29685 |