Related papers: A Lecture on Integration by Parts
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
Iterative peer grading activities may keep students engaged during in-class project presentations. Effective methods for collecting and aggregating peer assessment data are essential. Students tend to grade projects favorably. So, while…
Many annotation problems in computer vision can be phrased as integer linear programs (ILPs). The use of standard industrial solvers does not to exploit the underlying structure of such problems eg, the skeleton in pose estimation. The…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
Despite the success of branch-and-cut methods for solving mixed integer bilevel linear optimization problems (MIBLPs) in practice, there are still gaps in both the theory and practice surrounding these methods. In the first part of this…
We discuss some problems with the indefinite integral notation and the way of teaching of integrals in Calculus. Based on the discussion, and in order to avoid mistakes, we propose another notation for indefinite integrals.
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…
Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the…
Learning representations with diversified information remains as an open problem. Towards learning diversified representations, a new approach, termed Information Competing Process (ICP), is proposed in this paper. Aiming to enrich the…
Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to…
This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…
While many approaches have been proposed to analyze the problem of matrix multiplication parallel computing, few of them address the problem on heterogeneous processor platforms. It still remains an open question on heterogeneous processor…
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that…
Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e.,…
The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could…
It is well known that selecting a good Mixed Integer Programming (MIP) formulation is crucial for an effective solution with state-of-the art solvers. While best practices and guidelines for constructing good formulations abound, there is…