14 papers · ranked by Valyu relevance
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…
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.
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…
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…
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…
Nikita Doikov, Yurii Nesterov
In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate with regularization parameter proportional to the square root of the norm of the current gradient. For the basic scheme, as applied to the…
Alfonso Landeros, Oscar Hernan Madrid Padilla, Hua Zhou, Kenneth Lange
'Kenneth Lange'] The current paper studies the problem of minimizing a loss f(x) subject to constraints of the form Dx ∈ S, where S is a closed set, convex or not, and D is a matrix that fuses parameters. Fusion constraints can capture smoothness, sparsity, or more general constraint patterns. To tackle this generic…
Shikun Chen, Zebin Huang, Wenlong Zheng, Yuanchao Liu
Mathematical optimization is fundamental across many scientific and engineering applications. While data-driven models like gradient boosting and random forests excel at prediction tasks, they often lack mathematical regularity, being non-differentiable or even discontinuous. These models are commonly used to predict…
Lulu He, Yanan Du, Jianchao Bai
The conjugate gradient method is widely recognized as a foundational technique for large-scale unconstrained optimization. In this work, we introduce an Accelerated Stochastic Conjugate Gradient (ASCG) algorithm, specifically designed for a class of convex empirical risk minimization problems. The proposed ASCG method…
Yan Xia, Dandan Li, Songhua Wang, Mohamed Kamel Riahi
In this paper, a hybrid conjugate gradient projection method for finding solutions of constrained nonlinear equations is proposed by integrating both hyperplane projection and hybrid techniques. The key features of this method are as follows: (1) It is characterized by a low storage requirement and relies solely on…
Zelin Pei, Xiaoyu He, Yi Pan, Baichun Peng + 2 more
Black-box stochastic optimization involves sampling in both the solution and data spaces. Traditional variance reduction methods mainly designed for reducing the data sampling noise may suffer from slow convergence if the noise in the solution space is poorly handled. In this paper, we present a novel zeroth-order…
Chun Kit Jeffery Hou, Kamran Behdinan
Surrogate modeling has been popularized as an alternative to full-scale models in complex engineering processes such as manufacturing and computer-assisted engineering. The modeling demand exponentially increases with complexity and number of system parameters, which consequently requires higher-dimensional engineering…
Ali Fozooni, Osman Kamari, Mostafa Pourtalebiyan, Masoud Gorgich + 2 more
'Mohammad Khalilzadeh' 'Amin Valizadeh'] In this study, we evaluate several nongradient (evolutionary) search strategies for minimizing mathematical function expressions. We developed and tested the genetic algorithms, particle swarm optimization, and differential evolution in order to assess their general efficacy in…