12 papers · ranked by Valyu relevance
Anton Rodomanov, Yurii Nesterov
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational inequalities with monotone operator. Our algorithm can be seen as a combination of…
Natsuki Akaishi, Koki Yamada, Kohei Yatabe, Yuki Takayama + 1 more
'A. Borbély'] This paper proposes a phase-retrieval algorithm for X-ray ptychography with almost the same computational efficiency as the conventional methods. It exploits an optimization technique, subgradient projection, which has an interesting property that means it can be expected to avoid yielding poor images.
Yurii Nesterov
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on knowledge of the optimal value of the objective function, need corrections when they are applied to…
Q-L Dong, A Gibali, D Jiang, Y Tang
In this paper we study the bounded perturbation resilience of the extragradient and the subgradient extragradient methods for solving a variational inequality (VI) problem in real Hilbert spaces. This is an important property of algorithms which guarantees the convergence of the scheme under summable errors, meaning…
Kazuhiro Hishinuma, Hideaki Iiduka
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning algorithms incorporating the line search method, which automatically and…
Radu Ioan Boţ, Axel Böhm
We investigate the convergence properties of incremental mirror descent type subgradient algorithms for minimizing the sum of convex functions. In each step, we only evaluate the subgradient of a single component function and mirror it back to the feasible domain, which makes iterations very cheap to compute. The…
Mikhail A. Bragin, Emily L. Tucker
Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of integer decision variables, as the problem size increases, the number of possible…
Songnian He, Tao Wu
In the setting of Hilbert space, a modified subgradient extragradient method is proposed for solving Lipschitz-continuous and monotone variational inequalities defined on a level set of a convex function. Our iterative process is relaxed and self-adaptive, that is, in each iteration, calculating two metric projections…
Axel Böhm, Stephen J. Wright
We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that introduce less bias than the standard convex regularizers. We develop a variable…
Zhiwei Ai, Chenliang Li, Zheng Chen
The calculation of grasping force and displacement is important for multi-fingered stable grasping and research on slipping damage. By linearizing the friction cone, the robot multi-fingered grasping problem can be represented as a linear complementarity problem (LCP) with a saddle-point coefficient matrix. Because the…
Kai Xiong, Guanghui Zhao, Guangming Shi, Yingbin Wang
The Split Bregman method (SBM), a popular and universal CS reconstruction algorithm for inverse problems with both l1-norm and TV-norm regularization, has been extensively applied in complex domains through the complex-to-real transforming technique, e.g., MRI imaging and radar. However, SBM still has great potential…
Nadhir Ben Rached, Shyam Mohan Subbiah Pillai, Raúl Tempone, Yousri Slaoui + 1 more
'Yousri Slaoui' 'Solym Manou-Abi'] Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power-procurement schedule to minimize operating expenditure and the carbon footprint of cellular…