A Simple Method for Convex Optimization in the Oracle Model

Dadush, Daniel; Hojny, Christopher; Huiberts, Sophie; Weltge, Stefan

doi:10.1007/978-3-031-06901-7_12

Cited by 5 publications

(2 citation statements)

References 27 publications

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“…Besides its conceptual simplicity and distiction to existing methods for convex optimization in the SO model, we also regard it as a practical alternative. In fact, in terms of iterations, our vanilla implementation in Julia [49] performs similarly and often even better than the standard cut loop and the analytic center cutting plane method evaluated on a testbed of oracle-based linear optimization problems for matching problems, semidefinite relaxations of the maximum cut problem, and LPBoost. Moreover, the flexibility of our framework leaves several degrees of freedom to obtain optimized implementations that outperform our naive implementation.…”

Section: Introductionmentioning

confidence: 89%

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Geometric Aspects of Linear Programming

Huiberts¹

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Section: Introductionmentioning

confidence: 89%

“…We use the textbook implementation of the ellipsoid method, and Badenbroek's [10] implementation of the analytic center cutting plane method. Our method is implemented [49] in the spirit of Theorem 5.2.6, where 𝑝 𝑡 is computed using Gurobi.…”

Section: Computational Experimentsmentioning

confidence: 99%

Geometric Aspects of Linear Programming

Huiberts¹

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A Simple Method for Convex Optimization in the Oracle Model

Dadush

Hojny

Huiberts

et al. 2022

Integer Programming and Combinatorial Optimization

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A simple method for convex optimization in the oracle model

et al. 2023

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We give a simple and natural method for computing approximately optimal solutions for minimizing a convex function f over a convex set K given by a separation oracle. Our method utilizes the Frank–Wolfe algorithm over the cone of valid inequalities of K and subgradients of f. Under the assumption that f is L-Lipschitz and that K contains a ball of radius r and is contained inside the origin centered ball of radius R, using $$O\left( \frac{(RL)^2}{\varepsilon ^2} \cdot \frac{R^2}{r^2}\right) $$ O ( R L ) 2 ε 2 · R 2 r 2 iterations and calls to the oracle, our main method outputs a point $$x \in K$$ x ∈ K satisfying $$f(x) \le \varepsilon + \min _{z \in K} f(z)$$ f ( x ) ≤ ε + min z ∈ K f ( z ) . Our algorithm is easy to implement, and we believe it can serve as a useful alternative to existing cutting plane methods. As evidence towards this, we show that it compares favorably in terms of iteration counts to the standard LP based cutting plane method and the analytic center cutting plane method, on a testbed of combinatorial, semidefinite and machine learning instances.

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A Simple Method for Convex Optimization in the Oracle Model

Cited by 5 publications

References 27 publications

Geometric Aspects of Linear Programming

Geometric Aspects of Linear Programming

A Simple Method for Convex Optimization in the Oracle Model

A simple method for convex optimization in the oracle model

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