Related papers: Large-scale optimization with the primal-dual colu…
We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
The Primal-Dual Hybrid Gradient (PDHG) algorithm is a first-order method that can exploit GPUs to solve large-scale linear programming problems. The approach can often be faster than the alternatives, simplex and interior-point methods,…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
Decision trees are highly interpretable models for solving classification problems in machine learning (ML). The standard ML algorithms for training decision trees are fast but generate suboptimal trees in terms of accuracy. Other discrete…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization…
This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all…
In real-life applications, most optimization problems are variants of well-known combinatorial optimization problems, including additional constraints to fit with a particular use case. Usually, efficient algorithms to handle a restricted…
The Discrete Ordered Median Problem (DOMP) is formulated as a set partitioning problem using an exponential number of variables. Each variable corresponds to a set of demand points allocated to the same facility with the information of the…
The primal--dual hybrid gradient method (PDHGM, also known as the Chambolle--Pock method) has proved very successful for convex optimization problems involving linear operators arising in image processing and inverse problems. In this…
Column Generation (CG) is an iterative algorithm for solving linear programs (LPs) with an extremely large number of variables (columns). CG is the workhorse for tackling large-scale \textit{integer} linear programs, which rely on CG to…
Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…
Column generation is an iterative method used to solve a variety of optimization problems. It decomposes the problem into two parts: a master problem, and one or more pricing problems (PP). The total computing time taken by the method is…
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…
Several well-known algorithms in the field of combinatorial optimization can be interpreted in terms of the primal-dual method for solving linear programs. For example, Dijkstra's algorithm, the Ford-Fulkerson algorithm, and the Hungarian…
Continuous-time primal-dual gradient dynamics (PDGD) is an ubiquitous approach for dynamically solving constrained distributed optimization problems. Yet, the distributed nature of the dynamics makes it prone to communication uncertainties,…
In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity…
We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
In many practical applications of constrained optimization, scale and solving time limits make traditional optimization solvers prohibitively slow. Thus, the research question of how to design optimization proxies -- machine learning models…