# An objective-function-free algorithm for nonconvex stochastic optimization with deterministic equality and inequality constraints

arXiv: https://arxiv.org/abs/2603.29685 · HTML: https://mlsanity.com/paper/2603.29685/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [A unified convergence theory for adaptive first-order methods in the nonconvex case, including AdaNorm, full and diagonal AdaGrad and Muon](https://mlsanity.com/paper/2604.17423/) (2026)

## Abstract (arXiv)

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.