Variational Gram Functions: Convex Analysis and Optimization
نویسندگان
چکیده
منابع مشابه
Variational Gram Functions: Convex Analysis and Optimization
We propose a new class of convex penalty functions, called variational Gram functions (VGFs), that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. These functions can serve as regularizers in convex optimization problems arising from hierarchical classification, multitask learning, and estimating vectors with disjoint supports, among other applic...
متن کاملA Variational Method for Hyperbolically Convex Functions
In this paper we recall our variational method, based on Julia’s formula for the Hadamard variation, for hyperbolically convex polygons. We use this variational method to prove a general theorem for solving extremal problems for hyperbolically convex functions. Special cases of this theorem provide independent proofs for controlling growth and distortion for hyperbolically convex functions.
متن کاملBeyond Convex Optimization: Star-Convex Functions
We introduce a polynomial time algorithm for optimizing the class of star-convex functions, under no Lipschitz or other smoothness assumptions whatsoever, and no restrictions except exponential boundedness on a region about the origin, and Lebesgue measurability. The algorithm’s performance is polynomial in the requested number of digits of accuracy and the dimension of the search domain. This ...
متن کاملSolving asymmetric variational inequalities via convex optimization
Using duality, we reformulate the asymmetric variational inequality (VI) problem over a conic region as an optimization problem. We give sufficient conditions for the convexity of this reformulation. We thereby identify a class of VIs that includes monotone affine VIs over polyhedra, which may be solved by commercial optimization solvers. © 2005 Elsevier B.V. All rights reserved.
متن کاملConvex Analysis and Optimization with Submodular Functions: a Tutorial
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning [1, 2, 3, 4], computer vision [5, 6], operations research [7] or electrical networks [8]. Among these set-functions, submodular functions play an important role, similar to convex functions on vector spaces. In this tutorial, the theory of submodular functions is presented, in a self-contain...
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: SIAM Journal on Optimization
سال: 2017
ISSN: 1052-6234,1095-7189
DOI: 10.1137/16m1087424