Projection-Free Functional Constrained Optimization for Risk Aversion and Sparsity Control
Not on the map. Why?
Abstract (arXiv)
We study projection-free methods for functional constrained optimization with convex or smooth nonconvex objectives. Such problems arise in applications such as portfolio optimization and radiation therapy planning, where risk-aware criteria and sparsity frequently appear together. For the convex setting, we propose a Level Conditional Gradient (LCG) method that combines a level-set outer loop with a conditional gradient oracle for saddle-point subproblems, and we show an iteration complexity of Obig(ε-2log(ε-1)big) for smooth and nonsmooth cases without dependence on the magnitude of an optimal dual Lagrange multiplier. For the nonconvex setting, we propose the Inexact Proximal Point LCG (IPP-LCG) method, which solves a sequence of convex subproblems by LCG and attains Obig(ε-3log(ε-1)big) complexity for computing an ((ε,ε))-near-KKT point. Numerical results on portfolio selection and IMRT illustrate the practical sparsity/risk trade-offs of the proposed methods.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 14 of its 55 references that are in the map. First posted on arXiv 11 Oct 2022.
Builds on
14 of 55 references.
References · 14
- 2019Stochastic First-order Methods for Convex and Nonconvex Functional Constrained Optimizationcited by 38
- 2019Quadratically Regularized Subgradient Methods for Weakly Convex Optimization with Weakly Convex Constraintscited by 25
- 2016Frank-Wolfe Algorithms for Saddle Point Problemscited by 18
- 2018Complexity of a quadratic penalty accelerated inexact proximal point method for solving linearly constrained nonconvex composite programscited by 15
- 2016Structured Nonconvex and Nonsmooth Optimization: Algorithms and Iteration Complexity Analysiscited by 13
- 2017Non-convex Conditional Gradient Slidingcited by 12
- 2022Level Constrained First Order Methods for Function Constrained Optimizationcited by 8
- 2022CCCP is Frank-Wolfe in disguisecited by 8
- 2020Efficient Projection-Free Algorithms for Saddle Point Problemscited by 6
- 2016Level-set methods for convex optimizationcited by 5
- 2017Conditional Accelerated Lazy Stochastic Gradient Descentcited by 4
- 2020Conditional Gradient Methods for Convex Optimization with General Affine and Nonlinear Constraintscited by 4
Built on by
Citing papers per year: 2023: 2.
2 papers.