# An Adaptive Stochastic Sequential Quadratic Programming with Differentiable Exact Augmented Lagrangians

@article{Na2021AnAS, title={An Adaptive Stochastic Sequential Quadratic Programming with Differentiable Exact Augmented Lagrangians}, author={Sen Na and Mihai Anitescu and Mladen Kolar}, journal={ArXiv}, year={2021}, volume={abs/2102.05320} }

We consider solving nonlinear optimization problems with stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and…

## 6 Citations

### Inequality Constrained Stochastic Nonlinear Optimization via Active-Set Sequential Quadratic Programming

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This work proposes an active-set stochastic sequential quadratic programming algorithm that uses a differentiable exact augmented Lagrangian as the merit function, and adaptively selects the penalty parameters of the augmentedlagrangian, and performs Stochastic line search to decide the stepsize.

### Hessian Averaging in Stochastic Newton Methods Achieves Superlinear Convergence

- Computer Science, MathematicsMathematical Programming
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There exists a universal weighted averaging scheme that transitions to local convergence at an optimal stage, and still exhibits a superlinear convergence rate nearly (up to a logarithmic factor) matching that of uniform Hessian averaging.

### Inexact Sequential Quadratic Optimization for Minimizing a Stochastic Objective Function Subject to Deterministic Nonlinear Equality Constraints

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An algorithm that allows inexact subproblem solutions to be employed, which is particularly useful in large-scale settings when the matrices defining the subproblems are too large to form and/or factorize is proposed.

### A Stochastic Sequential Quadratic Optimization Algorithm for Nonlinear Equality Constrained Optimization with Rank-Deficient Jacobians

- Computer Science
- 2021

The proposed sequential quadratic optimization algorithm both allows the use of stochastic objective gradient estimates and possesses convergence guarantees even in the setting in which the constraint Jacobians may be rank deficient.

### A Fast Temporal Decomposition Procedure for Long-horizon Nonlinear Dynamic Programming

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We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP), with a differentiable…

### An Adaptive Sampling Sequential Quadratic Programming Method for Equality Constrained Stochastic Optimization

- Computer Science
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A practical adaptive inexact stochastic sequential quadratic programming (PAIS-SQP) method is described and criteria for controlling the sample size and the accuracy in the solutions of the SQP subproblems based on the variance estimates obtained as the optimization progresses is proposed.

### Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems

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- 2022

The global almost sure convergence guarantee for TR-StoSQP is established, and its empirical performance on both a subset of problems in the CUTEst test set and constrained logistic regression problems using data from the LIBSVM collection is illustrated.

### A Sequential Quadratic Programming Method with High Probability Complexity Bounds for Nonlinear Equality Constrained Stochastic Optimization

- Computer Science, Mathematics
- 2023

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems and a high-probability bound on the iteration complexity of the algorithm to approximate ﬁrst-order stationarity is derived.

### Accelerating Stochastic Sequential Quadratic Programming for Equality Constrained Optimization using Predictive Variance Reduction

- Computer Science, Mathematics
- 2022

Under reasonable assumptions, it is proved that a measure of ﬁrst-order stationarity evaluated at the iterates generated by the proposed algorithm converges to zero in expectation from arbitrary starting points, for both constant and adaptive step size strategies.

### Worst-Case Complexity of an SQP Method for Nonlinear Equality Constrained Stochastic Optimization

- Computer Science
- 2021

The overall complexity bound, which accounts for the adaptivity of the merit parameter sequence, shows that a result comparable to the unconstrained setting (with additional logarithmic factors) holds with high probability.

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