# A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming

arXiv: https://arxiv.org/abs/1804.08544 · HTML: https://mlsanity.com/paper/1804.08544/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2018.

## Built on by (most cited first, 14 of 14)

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- [Stochastic Constrained Decentralized Optimization for Machine Learning with Fewer Data Oracles: a Gradient Sliding Approach](https://mlsanity.com/paper/2404.02511/) (2024)
- [Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization](https://mlsanity.com/paper/2202.13212/) (2022)
- [Adaptive Lipschitz-Free Conditional Gradient Methods for Stochastic Composite Nonconvex Optimization](https://mlsanity.com/paper/2603.06369/) (2026)
- [Stochastic Compositional Optimization via Hybrid Momentum Frank--Wolfe](https://mlsanity.com/paper/2605.15350/) (2026)
- [Nonsmooth Projection-Free Optimization with Functional Constraints](https://mlsanity.com/paper/2311.11180/) (2023)
- [Federated Frank-Wolfe Algorithm](https://mlsanity.com/paper/2408.10090/) (2024)
- [ADMM for Structured Fractional Minimization](https://mlsanity.com/paper/2411.07496/) (2024)

## Abstract (arXiv)

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal O(1/√k) convergence rate. We demonstrate that the same rate holds if the linear subproblems are solved approximately with additive or multiplicative error. In contrast with the relevant work, we are able to characterize the convergence when the non-smooth term is an indicator function. Specific applications of our framework include the non-smooth minimization, semidefinite programming, and minimization with linear inclusion constraints over a compact domain. Numerical evidence demonstrates the benefits of our framework.