Search · four archives
Search · four archives
16 papers · ranked by Valyu relevance
Yujia Jin, Aaron Sidford, Kevin Tian
- (1) Separable minimax optimization. We study separable minimax optimization problems minx maxy f(x)−g(y)+h(x, y), where f and g have smoothness and strong convexity parameters (L x , µx ), (L y , µy ), and h is convex-concave with a (Λxx ,Λ xy ,Λ yy)-blockwise operator norm bounded Hessian. We provide an algorithm…
Hao Luo, Zihang Zhang
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential decay of a tailored Lyapunov function is established. Then several time…
Xiangkai Sun, Lijuan Zheng, Kok Lay Teo
dynamical systems for separable convex optimization Authors: ['Xiangkai Sun' 'Lijuan Zheng' 'Kok Lay Teo'] Abstract This paper deals with a Tikhonov regularized second-order plus first-order primaldual dynamical system with time scaling for separable convex optimization problems with linear equality constraints. This…
Bingsheng He, Shengjie Xu, Xiaoming Yuan
The alternating direction method of multipliers (ADMM) proposed by Glowinski and Marrocco is a benchmark algorithm for two-block separable convex optimization problems with linear equality constraints. It has been modified, specified, and generalized from various perspectives to tackle more concrete or complicated…
Koen Ligthart
We consider the periodic behavior of the value functions $b\mapsto\min\{f(x)\ \vert\ Ax=b,\,x\in\mathbb Z_{\ge0}^n\}$ of integer programs. We show that there exists a positive integer $M$ depending only on the constraint matrix $A\in\mathbb Z^{m\times n}$ so that the value function is convex extensible on any subdomain…
Nicholas Moehle, Jack Gindi, Stephen Boyd, Mykel J. Kochenderfer
Mean–variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum nonzero position and trade sizes. We propose a heuristic algorithm for such problems based on the alternating direction method of multipliers (ADMM). This…
Jan Kronqvist, Ruth Misener, Calvin Tsay
We develop a class of mixed-integer formulations for disjunctive constraints intermediate to the big-M and convex hull formulations in terms of relaxation strength. The main idea is to capture the best of both the big-M and convex hull formulations: a computationally light formulation with a tight relaxation. The…
Peter Gangl, Nico Nees, Michael Stingl
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models constructed from convex separable first order approximations have a long and successful…
Omar M. Sleem, M.E. Ashour, N. S. Aybat, Constantino M. Lagoa
Sparsity finds applications in diverse areas such as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts and need less storage. This paper proposes a heuristic method for retrieving sparse approximate solutions of optimization…
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…
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…
Vishal Rana, Jianhao Peng, Chao Pan, Hanbaek Lyu + 3 more
Dictionary learning (DL), implemented via matrix factorization (MF), is commonly used in computational biology to tackle ubiquitous clustering problems. The method is favored due to its conceptual simplicity and relatively low computational complexity. However, DL algorithms produce results that lack interpretability…
Yiang Pan, Yuanjing Feng, Jianzhong He, William Consagra + 3 more
Diffusion MRI (dMRI) enables noninvasive characterization of white-matter fiber orientations and tissue microstructure, but widely used approaches, such as constrained spherical deconvolution (CSD) and parametric multicompartment models, typically address these features separately. The diffusion tensor distribution…
Anton V. Sinitskiy
In this paper, we extend our previous work on a simplified model of the nervous system by solving the general optimization problem for the evolutionary cost of the nervous system. This optimization takes into account constraints on the scales of membrane potential kinetics and sensory response function to ensure…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
Charlotte Merzbacher, Oisin Mac Aodha, Diego A. Oyarzún
Recent advances in synthetic biology have enabled the construction of molecular circuits that operate across multiple scales of cellular organization, such as gene regulation, signalling pathways and cellular metabolism. Computational optimization can effectively aid the design process, but current methods are…