Related papers: New Methods for Solving Large Scale Linear Program…
We study the problem of solving linear program in the streaming model. Given a constraint matrix $A\in \mathbb{R}^{m\times n}$ and vectors $b\in \mathbb{R}^m, c\in \mathbb{R}^n$, we develop a space-efficient interior point method that…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
In optimization routines used for on-line Model Predictive Control (MPC), linear systems of equations are usually solved in each iteration. This is true both for Active Set (AS) methods as well as for Interior Point (IP) methods, and for…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
Several well known large scale linear programming decomposition methodologies exist. Benders Decomposition, which covers the case where some small subset of variables link the otherwise separable subproblems. Dantzig-Wolfe decomposition and…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
It has been verified that the linear programming (LP) is able to formulate many real-life optimization problems, which can obtain the optimum by resorting to corresponding solvers such as OptVerse, Gurobi and CPLEX. In the past decades, a…
Automatic software system optimization can improve software speed, reduce operating costs, and save energy. Traditional approaches to optimization rely on manual tuning and compiler heuristics, limiting their ability to generalize across…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
The Big Data phenomenon has spawned large-scale linear programming problems. In many cases, these problems are non-stationary. In this paper, we describe a new scalable algorithm called NSLP for solving high-dimensional, non-stationary…
Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or…
Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
Interior-point methods are state-of-the-art algorithms for solving linear programming (LP) problems with polynomial complexity. Specifically, the Karmarkar algorithm typically solves LP problems in time O(n^{3.5}), where $n$ is the number…
Large scale parameter estimation problems are among some of the most computationally demanding problems in numerical analysis. An academic researcher's domain-specific knowledge often precludes that of software design, which results in…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
Previous works suggested the use of Branch and Bound techniques for finding the optimal allocation in (multi-unit) combinatorial auctions. They remarked that Linear Programming could provide a good upper-bound to the optimal allocation, but…
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…
Increasing the complexity of solving budgetary allocation (NP-hardness problem) has led a wide range of methods to minimize the costs. Metaheuristics and Linear Programming (LP) are the most optimization in this fields. Therefore, this…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…