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Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
The ELM method has become widely used for classification and regressions problems as a result of its accuracy, simplicity and ease of use. The solution of the hidden layer weights by means of a matrix pseudoinverse operation is a…
We present a high-performance budgeted multi-level Monte Carlo method for estimates on the entire spatial domain of multi-PDE problems with random input data. The method is designed to operate optimally within memory and CPU-time…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
The framework of Integral Quadratic Constraints (IQC) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to a semi-definite program (SDP). In the case of over-relaxed Alternating Direction…
We propose a single-loop variance-reduced acceleration framework, which relates checkpoint update probabilities to momentum parameters, for solving the composite general convex problem where the smooth part has the finite-sum structure.…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined by sum-of-squares (SOS) convex polynomials. These problems…
We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…
The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…
This paper studies exact semidefinite programming relaxations (SDPRs) for separable quadratically constrained quadratic programs (QCQPs). We consider the construction of a larger separable QCQP from multiple QCQPs with exact SDPRs. We show…
Quality-Diversity (QD) optimization algorithms are a well-known approach to generate large collections of diverse and high-quality solutions. However, derived from evolutionary computation, QD algorithms are population-based methods which…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…
We present a new parallel computational framework for the efficient solution of a class of $L^2$/$L^1$-regularized optimal control problems governed by semi-linear elliptic partial differential equations (PDEs). The main difficulty in…
We introduce fast randomized algorithms for solving semidefinite programming (SDP) relaxations of the partial permutation synchronization (PPS) problem, a core task in multi-image matching with significant relevance to 3D reconstruction.…
Value iteration is a well-known method of solving Markov Decision Processes (MDPs) that is simple to implement and boasts strong theoretical convergence guarantees. However, the computational cost of value iteration quickly becomes…
Permutation symmetries of deep networks make basic operations like model merging and similarity estimation challenging. In many cases, aligning the weights of the networks, i.e., finding optimal permutations between their weights, is…