Related papers: Three methods, one problem: Classical and AI appro…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
Phasor Measurement Units (PMUs) are essential measuring devices for monitoring, control and protection of power systems. The objective of the optimal PMU placement (OPP) problem is to minimize the number of PMUs and select the bus locations…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
Integer programming (IP) has proven to be highly effective in solving many path-based optimization problems in robotics. However, the applications of IP are generally done in an ad-hoc, problem specific manner. In this work, after examined…
Large language models have demonstrated remarkable capabilities, but their performance is heavily reliant on effective prompt engineering. Automatic prompt optimization (APO) methods are designed to automate this and can be broadly…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
We present a set of integer programs (IPs) for the Steiner tree problem with the property that the best solution obtained by solving all, provides an optimal Steiner tree. Each IP is polynomial in the size of the underlying graph and our…
We introduce a novel hybrid quantum-classical variational optimization method for unconstrained binary combinatorial optimization problems on gate-model quantum computers, integrating a custom variational ansatz, staged feedback-based dual…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
We study a type of Online Linear Programming (OLP) problem that maximizes the objective function with stochastic inputs. The performance of various algorithms that analyze this type of OLP is well studied when the stochastic inputs follow…
In this article, we apply a new methodology for precision tuning to the N-body problem. Our technique, implemented in a tool named POP, makes it possible to optimize the numerical data types of a program performing floating-point…
In this paper we present a novel numerical method for computing local minimizers of twice smooth differentiable non-linear programming (NLP) problems. So far all algorithms for NLP are based on either of the following three principles:…
The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is…
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…
Polyhedral compilers can perform complex loop optimizations that improve parallelism and cache behaviour of loops in the input program. These transformations result in significant performance gains on modern processors which have large…
AI methods, such as generative models and reinforcement learning, have recently been applied to combinatorial optimization (CO) problems, especially NP-hard ones. This paper compares such GPU-based methods with classical CPU-based methods…
Using a constraint satisfaction approach, we exhibit configurations of $2n$ points on the $n\times n$ grid for all $n\le60$ with no three collinear. Consequently, the smallest $n$ for which it is unknown whether $D(n)=2n$ increases from…
This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…
We present an algorithm for a class of $n$-fold ILPs: whose existing algorithms in literature typically (1) are based on the \textit{augmentation framework} where one starts with an arbitrary solution and then iteratively moves towards an…