Related papers: Opt: A Domain Specific Language for Non-linear Lea…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
This paper introduces the design and implementation of PyOptInterface, a modeling language for mathematical optimization embedded in Python programming language. PyOptInterface uses lightweight and compact data structure to bridge…
Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the…
Optimal power flow problems (OPFs) are mathematical programs used to determine how to distribute power over networks subject to network operation constraints and the physics of power flows. In this work, we take the view of treating an OPF…
Emerging artificial intelligence applications across the domains of computer vision, natural language processing, graph processing, and sequence prediction increasingly rely on deep neural networks (DNNs). These DNNs require significant…
Optimal power flow (OPF) over power transmission networks poses challenging large-scale nonlinear optimization problems, which involve a large number of quadratic equality and indefinite quadratic inequality constraints. These…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
Optimization problems are pervasive across various sectors, from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers, as the…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Optimization models have been applied to solve a wide variety of decision-making problems. These models are usually developed by optimization experts but are used by practitioners without optimization expertise in various application…
We propose a reduced-space formulation for optimizing over trained neural networks where the network's outputs and derivatives are evaluated on a GPU. To do this, we treat the neural network as a "gray box" where intermediate variables and…
Achieving a desirable balance between rendering quality and real-time performance is a long-standing challenge in modern game and rendering engines, particularly on resource-constrained mobile devices such as laptops, tablets, and…
This paper shows that the optimal subgradient algorithm, OSGA, proposed in \cite{NeuO} can be used for solving structured large-scale convex constrained optimization problems. Only first-order information is required, and the optimal…
Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled…
Traditional algorithms for stochastic optimization require projecting the solution at each iteration into a given domain to ensure its feasibility. When facing complex domains, such as positive semi-definite cones, the projection operation…
Efficiently solving Optimal Power Flow (OPF) problems in power systems is crucial for operational planning and grid management. There is a growing need for scalable algorithms capable of handling the increasing variability, constraints, and…
Real-world vision-language applications demand varying levels of perceptual granularity. However, most existing visual large language models (VLLMs), such as LLaVA, pre-assume a fixed resolution for downstream tasks, which leads to subpar…
This paper presents a novel, high-performance, graphical processing unit-based algorithm for efficiently solving two-dimensional linear programs in batches. The domain of two-dimensional linear programs is particularly useful due to the…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining pre-defined functions and sets. MathOptInterface is significantly more general than existing data structures in…