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We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
In this paper, we show the effectiveness of a pipeline implementation of Dynamic Programming (DP) on GPU. As an example, we explain how to solve a matrix-chain multiplication (MCM) problem by DP on GPU. This problem can be sequentially…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
Utilizing GPUs is critical for high performance on heterogeneous systems. However, leveraging the full potential of GPUs for accelerating legacy CPU applications can be a challenging task for developers. The porting process requires…
To obtain a better understanding of the trade-offs between various objectives, Bi-Objective Integer Programming (BOIP) algorithms calculate the set of all non-dominated vectors and present these as the solution to a BOIP problem.…
Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…
Graphics Processing Units (GPUs) with high computational capabilities used as modern parallel platforms to deal with complex computational problems. We use this platform to solve large-scale linear programing problems by revised simplex…
We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for…
The paper considers the problem of scheduling software modules on a multi-core processor, taking into account the limited bandwidth of the data bus and the precedence constraints. Two problem formulations with different levels of…
We introduce Breadth-First Pipeline Parallelism, a novel training schedule which optimizes the combination of pipeline and data parallelism. Breadth-First Pipeline Parallelism lowers training time, cost and memory usage by combining a high…
Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that…
Data-intensive, graph-based computations are pervasive in several scientific applications, and are known to to be quite challenging to implement on distributed memory systems. In this work, we explore the design space of parallel algorithms…
Mixed-integer programming (MIP) extends linear programming by incorporating both continuous and integer decision variables, making it widely used in production planning, logistics scheduling, and resource allocation. However, MIP remains…
Convex quadratic programming (QP) is an essential class of optimization problems with broad applications across various fields. Traditional QP solvers, typically based on simplex or barrier methods, face significant scalability challenges.…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
This paper proposes a novel primal heuristic for Mixed Integer Programs, by employing machine learning techniques. Mixed Integer Programming is a general technique for formulating combinatorial optimization problems. Inside a solver, primal…
In recent years, there has been renewed interest in closing the performance gap between state-of-the-art planning solvers and generalized planning (GP), a research area of AI that studies the automated synthesis of algorithmic-like…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant…