High-precision linear minimization is no slower than projection
Abstract
Abstract This note demonstrates that, for all compact convex sets, high-precision linear minimization can be performed via a single evaluation of the projection and a scalar-vector multiplication. In consequence, if $$\varepsilon $$ -approximate linear minimization takes at least $$L(\varepsilon )$$ real vector-arithmetic operations and projection requires P operations, then $$\mathcal {O}(P)\ge \mathcal {O}(L(\varepsilon ))$$ is guaranteed. This concept is expounded with examples, an explicit error bound, and an exact linear minimization result for polyhedral sets.
Fields of Study & Subjects
Advanced Optimization Algorithms Research
Optimization and Variational Analysis
Numerical Methods and Algorithms
Publication details
- Journal / source
- Optimization Letters
- Volume
- 20
- Issue
- 4
- Pages
- 909–915
- Publication date
- 5 January 2026
- Language
- EN