Related papers: Non-uniform Grid Refinement for the Combinatorial …
We introduce and study the combinatorial optimization problem with interaction costs (COPIC). COPIC is the problem of finding two combinatorial structures, one from each of two given families, such that the sum of their independent linear…
Due to the limited connectivity of gate model quantum devices, logical quantum circuits must be compiled to target hardware before they can be executed. Often, this process involves the insertion of SWAP gates into the logical circuit,…
We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to…
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…
Domain decomposition methods are widely used and effective in the approximation of solutions to partial differential equations. Yet the optimal construction of these methods requires tedious analysis and is often available only in…
For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to…
This paper studies an acceleration technique for incremental aggregated gradient ({\sf IAG}) method through the use of \emph{curvature} information for solving strongly convex finite sum optimization problems. These optimization problems of…
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical…
We consider the minimum-energy control of a car, which is modelled as a point mass sliding on the ground in a fixed direction, and so it can be mathematically described as the double integrator. The control variable, representing the…
Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is…
Nonlinear constrained optimization has a wide range of practical applications. In this paper, we consider nonlinear optimization with inequality constraints. The interior point method is considered to be one of the most powerful algorithms…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
As a quantum-inspired, non-traditional analog solver architecture, the analog Ising machine (AIM) has emerged as a distinctive computational paradigm to address the rapidly growing demand for computational power. However, the mathematical…
In optimal control problem, policy iteration (PI) is a powerful reinforcement learning (RL) tool used for designing optimal controller for the linear systems. However, the need for an initial stabilizing control policy significantly limits…
The computational kernel in solving the $S_N$ transport equations is the parallel sweep, which corresponds to directly inverting a block lower triangular linear system that arises in discretizations of the linear transport equation.…
We study the stochastic optimization of canonical correlation analysis (CCA), whose objective is nonconvex and does not decouple over training samples. Although several stochastic gradient based optimization algorithms have been recently…