Related papers: Revisiting Tardos's Framework for Linear Programmi…
Following the breakthrough work of Tardos in the bit-complexity model, Vavasis and Ye gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix. For…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…
In this paper we present a new algorithm for solving linear programs that requires only $\tilde{O}(\sqrt{rank(A)}L)$ iterations to solve a linear program with $m$ constraints, $n$ variables, and constraint matrix $A$, and bit complexity…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
In this paper we provide an $\tilde{O}(nd+d^{3})$ time randomized algorithm for solving linear programs with $d$ variables and $n$ constraints with high probability. To obtain this result we provide a robust, primal-dual…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
We study the design of polylogarithmic depth algorithms for approximately solving packing and covering semidefinite programs (or positive SDPs for short). This is a natural SDP generalization of the well-studied positive LP problem.…
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…
We consider integer and linear programming problems for which the linear constraints exhibit a (recursive) block-structure: The problem decomposes into independent and efficiently solvable sub-problems if a small number of constraints is…
Least-absolute-deviations (LAD) line fitting is robust to outliers but computationally more involved than least squares regression. Although the literature includes linear and near-linear time algorithms for the LAD line fitting problem,…
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…
While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the…
Interior point algorithms for solving linear programs have been studied extensively for a long time [e.g. Karmarkar 1984; Lee, Sidford FOCS'14; Cohen, Lee, Song STOC'19]. For linear programs of the form $\min_{Ax=b, x \ge 0} c^\top x$ with…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives…
Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all…