Related papers: An optimization-based reformulation of the classic…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
Stochastic resetting, the procedure of stopping and re-initializing random processes, has recently emerged as a powerful tool for accelerating processes ranging from queuing systems to molecular simulations. However, its usefulness is…
In terms of the concepts of state and state transition, a new algorithm-State Transition Algorithm (STA) is proposed in order to probe into classical and intelligent optimization algorithms. On the basis of state and state transition, it…
State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions.…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…
This work explores the global optimization problem of finding lowest-energy configurations (ground states) in disordered continuous spins models from statistical physics, with a particular focus on the random field XY model. Due to an…
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and…
The Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced, using incremental updates to scale to large datasets, and using Monte Carlo (MC)…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Economic dispatch problem for a networked power system has been considered. The objective is to minimize the total generation cost while meeting the overall supply-demand balance and generation capacity. In particular, a more practical…
This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state…
This paper presents a novel approach to solving large-scale minimax problems with nonsmooth regularizers. We propose a stochastic implicit proximal point algorithm with variance reduction techniques where stochastic oracles are selected in…
Reconstruction techniques are commonly used in cosmology to reduce complicated nonlinear behaviours to a more tractable linearized system. We study a new reconstruction technique that uses the Moving-Mesh algorithm to estimate the…