Related papers: Duality Gap in Interval Linear Programming
Dantzig and Eaves claimed that fundamental duality theorems of linear programming were a trivial consequence of Fourier elimination. Another property of Fourier elimination is considered here, regarding the existence of implicit equalities…
This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality…
In this paper, our goal is to study fundamental foundations of linear quadratic Gaussian (LQG) control problems for stochastic linear time-invariant systems via Lagrangian duality of semidefinite programming (SDP) problems. In particular,…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
In this article, we develop duality principles applicable to primal variational formulations found in the non-linear elasticity theory. As a first application, we establish the concerning results in details for one and three-dimensional…
We prove a duality relation and an integration by parts formula for fractional operators with a general analytical kernel. Based on these basic results, we are able to prove a new Gronwall's inequality and continuity and differentiability…
Duality of linear programming is a standard approach to the classical weighted maximum matching problem. From an economic perspective, the dual variables can be regarded as prices of products and payoffs of buyers in a two-sided matching…
With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems.…
Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of…
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition.…
Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence…
We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to…
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the…
We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
A new approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin's duality…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
For a binary integer program (IP) ${\rm max} ~ c^\mathsf{T} x, Ax \leq b, x \in \{0,1\}^n$, where $A \in \mathbb{R}^{m \times n}$ and $c \in \mathbb{R}^n$ have independent Gaussian entries and the right-hand side $b \in \mathbb{R}^m$…
This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…