Related papers: An Efficient Polynomial Interior-Point Algorithm f…
In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central…
We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce…
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 primal-dual interior point method (IPM) is widely regarded as the most efficient IPM variant for linear optimization. In this paper, we demonstrate that the improved stability of the pure primal IPM can allow speedups relative to a…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
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…
$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…
The most efficient algorithms for finding maximum independent sets in both theory and practice use reduction rules to obtain a much smaller problem instance called a kernel. The kernel can then be solved quickly using exact or heuristic…
While previous work on energy-efficient algorithms focused on assumption that tasks can be assigned to any processor, we initially study the problem of task scheduling on restricted parallel processors. The objective is to minimize the…
This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…
Conic optimization plays a crucial role in many machine learning (ML) problems. However, practical algorithms for conic constrained ML problems with large datasets are often limited to specific use cases, as stochastic algorithms for…
In this paper, we describe the hyper-parameter search problem in the field of machine learning and present a heuristic approach in an attempt to tackle it. In most learning algorithms, a set of hyper-parameters must be determined before…
In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
Executing various sequences of system functions in a system under test represents one of the primary techniques in software testing. The natural way to create effective, consistent and efficient test sequences is to model the system under…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…