Search
Search Results
-
Bounding the Inefficiency via the Primal-Dual Method
The main tool used to show all the results in this book is the primal-dual method. Introduced by Bil`o [22], this framework is based on the...
-
Primal-Dual Simplex Method
Methods perform very differently when solving the same problem. It is a common case that a problem that is solved slowly by the simplex method would...
-
Improved Approximation Algorithms by Generalizing the Primal-Dual Method Beyond Uncrossable Functions
We address long-standing open questions raised by Williamson, Goemans, Vazirani and Mihail pertaining to the design of approximation algorithms for...
-
Multi-consensus decentralized primal-dual fixed point algorithm for distributed learning
Decentralized distributed learning has recently attracted significant attention in many applications in machine learning and signal processing. To...
-
Preconditioned golden ratio primal-dual algorithm with linesearch
The golden ratio primal-dual algorithm (GRPDA) was proposed for solving the saddle point problems which are being widely used in a variety of areas....
-
Parallel Primal-dual Method with Application to Image Restoration
As inverse problems, most image restoration algorithms involve linear inverse operator. When processing multichannel images, the inverse operation is...
-
A linear primal–dual multi-instance SVM for big data classifications
Multi-instance learning (MIL) handles data that is organized into sets of instances known as bags. Traditionally, MIL is used in the...
-
A New Prediction–Correction Primal–Dual Hybrid Gradient Algorithm for Solving Convex Minimization Problems with Linear Constraints
The primal–dual hybrid gradient (PDHG) algorithm has been applied for solving linearly constrained convex problems. However, it was shown that...
-
A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is...
-
Primal–Dual Algorithms for Distributed Economic Dispatch
In this chapter, we study a distributed primal–dual gradient algorithm applicable in a sequence of time-varying general directed networks based on a...
-
A Quasi-Newton Primal-Dual Algorithm with Line Search
Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as...
-
Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems
In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the...
-
Extending the Primal-Dual 2-Approximation Algorithm Beyond Uncrossable Set Families
A set family \(\mathcal{F}\) is uncrossable if...
-
\(O(1/k^2)\) convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming
The recent balanced augmented Lagrangian method (ALM) and its dual-primal version are effective for solving linearly constrained convex programming...
-
Improved Lattice Enumeration Algorithms by Primal and Dual Reordering Methods
The security of lattice-based cryptosystems is generally based on the hardness of the Shortest Vector Problem (SVP). There are two common categories...
-
Dual Deficient-Basis Method
This chapter attacks the standard LP problem from the dual side using the deficient basis. To achieve optimality, the method presented in the...
-
An MP-DWR method for h-adaptive finite element methods
In a dual-weighted residual method based on the finite element framework, the Galerkin orthogonality is an issue that prevents solving the dual...
-
Linear Programming Computation
This monograph represents a historic breakthrough in the field of linear programming (LP)since George Dantzig first discovered the simplex method in...
-
Duality Principle and Dual Simplex Method
Duality is an essential part of LP theory. It is related to the special relationship between one LP problem and another, both of which involve the...
-
A first-order inexact primal-dual algorithm for a class of convex-concave saddle point problems
In this paper, we study a first-order inexact primal-dual algorithm (I-PDA) for solving a class of convex-concave saddle point problems. The I-PDA,...
