Convergence of first-order methods via the convex conjugate
نویسندگان
چکیده
منابع مشابه
First-order Methods for Geodesically Convex Optimization
Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the understanding of g-convex optimization by developing iteration complexity analysis for several first-order algorithms on Hadamard manifolds. Specifically, we prove ...
متن کاملFirst-order methods with inexact oracle: the strongly convex case
The goal of this paper is to study the effect of inexact first-order information on the first-order methods designed for smooth strongly convex optimization problems. It can be seen as a generalization to the strongly convex case of our previous paper [1]. We introduce the notion of (!,L,μ)-oracle, that can be seen as an extension of the (!,L)-oracle (previously introduced in [1]), taking into ...
متن کاملFirst-order methods of smooth convex optimization with inexact oracle
In this paper, we analyze different first-order methods of smooth convex optimization employing inexact first-order information. We introduce the notion of an approximate first-order oracle. The list of examples of such an oracle includes smoothing technique, Moreau-Yosida regularization, Modified Lagrangians, and many others. For different methods, we derive complexity estimates and study the ...
متن کاملIteration-complexity of first-order penalty methods for convex programming
This paper considers a special but broad class of convex programming (CP) problems whose feasible region is a simple compact convex set intersected with the inverse image of a closed convex cone under an affine transformation. It studies the computational complexity of quadratic penalty based methods for solving the above class of problems. An iteration of these methods, which is simply an iter...
متن کاملFast First-Order Methods for Composite Convex Optimization with Backtracking
We propose new versions of accelerated first order methods for convex composite optimization, where the prox parameter is allowed to increase from one iteration to the next. In particular we show that a full backtracking strategy can be used within the FISTA [1] and FALM algorithms [7] while preserving their worst-case iteration complexities of O( √ L(f)/ ). In the original versions of FISTA an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Operations Research Letters
سال: 2017
ISSN: 0167-6377
DOI: 10.1016/j.orl.2017.08.013