# Self-adaptive algorithms for quasiconvex programming and applications to machine learning

arXiv: https://arxiv.org/abs/2212.06379 · HTML: https://mlsanity.com/paper/2212.06379/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 13 Dec 2022.

## Builds on (most cited first, 5 of 5)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Adaptive Gradient Descent without Descent](https://mlsanity.com/paper/1910.09529/) (2019)
- [Convergence Rates of Subgradient Methods for Quasi-convex Optimization Problems](https://mlsanity.com/paper/1910.10879/) (2019)
- [Simplified Versions of the Conditional Gradient Method](https://mlsanity.com/paper/1801.05251/) (2018)
- [On the Frank-Wolfe algorithm for non-compact constrained optimization problems](https://mlsanity.com/paper/2101.08830/) (2021)

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

- [A Hyper-Transformer model for Controllable Pareto Front Learning with Split Feasibility Constraints](https://mlsanity.com/paper/2402.05955/) (2024)

## Abstract (arXiv)

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach under mild assumptions. Specifically, the objective function may not satisfy the convexity condition. Unlike descent line-search algorithms, it does not need a known Lipschitz constant to figure out how big the first step should be. The crucial feature of this process is the steady reduction of the step size until a certain condition is fulfilled. In particular, it can provide a new gradient projection approach to optimization problems with an unbounded constrained set. The correctness of the proposed method is verified by preliminary results from some computational examples. To demonstrate the effectiveness of the proposed technique for large-scale problems, we apply it to some experiments on machine learning, such as supervised feature selection, multi-variable logistic regressions and neural networks for classification.