Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
New Analysis of an Away-Step Frank–Wolfe Method for Minimizing Log-Homogeneous Barriers. |
| Συγγραφείς: |
Zhao, Renbo1 (AUTHOR) renbo-zhao@uiowa.edu |
| Πηγή: |
Mathematics of Operations Research (INFORMS). Feb2026, Vol. 51 Issue 1, p35-59. 25p. |
| Θεματικοί όροι: |
*Stochastic processes, Optimization algorithms, Optimal designs (Statistics), Numerical analysis, Convex programming, Mathematical regularization |
| Περίληψη: |
We present and analyze an away-step Frank–Wolfe method for the convex optimization problem minx∈X f(Ax)+〈c,x〉 , where f is a θ-logarithmically homogeneous self-concordant barrier, A is a linear operator that may be noninvertible, 〈c,·〉 is a linear function, and X is a nonempty polytope. The applications of primary interest include D-optimal design, inference of multivariate Hawkes processes, and total variation-regularized Poisson image deblurring. We establish affine-invariant and norm-independent global linear convergence rates of our method in terms of both the objective gap and the Frank–Wolfe gap. When specialized to the D-optimal design problem, our results settle a question left open since Ahipasaoglu et al. [Ahipasaoglu SD, Sun P, Todd MJ (2008) Linear convergence of a modified Frank–Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Optim. Methods Software 23(1):5–19]. We also show that the iterates generated by our method will land on and remain in a face of X within a bounded number of iterations, which can lead to improved local linear convergence rates (for both the objective gap and the Frank–Wolfe gap). We conduct numerical experiments on D-optimal design and inference of multivariate Hawkes processes, and our results not only demonstrate the efficiency and effectiveness of our method compared with other principled first-order methods but also, corroborate our theoretical results quite well. Funding: This work was supported by the Air Force Office of Scientific Research [Grant FA9550-22-1-0356]. [ABSTRACT FROM AUTHOR] |
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