Related papers: Continuous-Time Systems for Solving 0-1 Integer Li…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
This paper studies a formulation of 1-bit Compressed Sensing (CS) problem based on the maximum likelihood estimation framework. In order to solve the problem we apply the recently proposed Gradient Support Pursuit algorithm, with a minor…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a…
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…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
We study the general integer programming (IP) problem of optimizing a separable convex function over the integer points of a polytope: $\min \{f(\mathbf{x}) \mid A\mathbf{x} = \mathbf{b}, \, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \,…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…
The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether…
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…
Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…
In this paper, we describe a novel approach for checking safety specifications of a dynamical system with exogenous inputs over infinite time horizon that is guaranteed to terminate in finite time with a conclusive answer. We introduce the…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…
The Unbounded Knapsack Problem (UKP) is a well-known variant of the famous 0-1 Knapsack Problem (0-1 KP). In contrast to 0-1 KP, an arbitrary number of copies of every item can be taken in UKP. Since UKP is NP-hard, fully polynomial time…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…