相关论文: Faster and more accurate computation of the $\math…

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…

We address the problems of computing operator norms of matrices induced by given norms on the argument and the image space. It is known that aside of a fistful of "solvable cases," most notably, the case when both given norms are Euclidean,…

In this paper, we propose two novel algorithms for histogram specification and quantile transformation of data without local information. These are core techniques that can serve as building blocks for applications that require specifying…

Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing…

This work presents a new approach for simulating the HHL linear systems of equations solver algorithm with tensor networks. First, a novel HHL in the qudits formalism, the generalization of qubits, is developed, and then its operations are…

The growing amount of high dimensional data in different machine learning applications requires more efficient and scalable optimization algorithms. In this work, we consider combining two techniques, parallelism and Nesterov's…

Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…

For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…

An algorithm is presented for momentum gradient descent optimization based on the first-order differential equation of the Newtonian dynamics. The fictitious mass is introduced to the dynamics of momentum for regularizing the adaptive…

Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…

By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…

This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…

An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations…

Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…

We develop randomized matrix-free algorithms for estimating partial traces, a generalization of the trace arising in quantum physics and chemistry. Our algorithm improves on the typicality-based approach used in [T. Chen and Y-C. Cheng,…

In this paper, we present a novel maximum entropy formulation of the Differential Dynamic Programming algorithm and derive two variants using unimodal and multimodal value functions parameterizations. By combining the maximum entropy…

Optimizing multiple competing objectives is a common problem across science and industry. The inherent inextricable trade-off between those objectives leads one to the task of exploring their Pareto front. A meaningful quantity for the…

This paper proposes a stochastic variant of a classic algorithm---the cubic-regularized Newton method [Nesterov and Polyak 2006]. The proposed algorithm efficiently escapes saddle points and finds approximate local minima for general…

We introduce a randomized algorithm for computing the minimal-norm solution to an underdetermined system of linear equations. Given an arbitrary full-rank m x n matrix A with m<n, any m x 1 vector b, and any positive real number epsilon…

An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the…