相关论文: Direct transcription methods based on fractional i…

We study the problem of finding an $\epsilon$-first-order stationary point (FOSP) of a smooth function, given access only to gradient information. The best-known gradient query complexity for this task, assuming both the gradient and…

Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of values rather than being just a fixed integer/fraction as it…

We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. The key points…

This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The…

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…

This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…

Orthogonal collocation methods are direct approaches for solving optimal control problems (OCP). A high solution accuracy is achieved with few optimization variables, making it more favorable for embedded and real-time NMPC applications.…

We present a novel method to approximate optimal feedback laws for nonlinear optimal control based on low-rank tensor train (TT) decompositions. The approach is based on the Dirac-Frenkel variational principle with the modification that the…

We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem…

An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…

This paper studies exact linearization methods for stochastic SISO affine controlled dynamical systems. The systems are defined as vectorfield triplets in Euclidean space. The goal is to find, for a given nonlinear stochastic system, a…

This paper proposes real-time sequential convex programming (RTSCP), a method for solving a sequence of nonlinear optimization problems depending on an online parameter. We provide a contraction estimate for the proposed method and, as a…

In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…

The direct simulation Monte Carlo (DSMC) method is widely used to describe rarefied gas flows. The DSMC method accounts for the transport and collisions of computational particles, resulting in higher computational costs in the continuum…

The article proposes a Caputo fractional conjugate gradient (CFCG) method for unconstrained optimization problems which is applicable to smooth as well as non-smooth problmes. The proposed method uses a non-adaptive version of the Caputo…

We introduce the MATLAB-based software QuITO (Quasi-Interpolation based Trajectory Optimization) to numerically solve a wide class of constrained nonlinear optimal control problems (OCP). The solver is based on the QuITO (the same…

This article introduces a new transcription, change point localization, and mesh refinement scheme for direct optimization-based solutions and for uniform approximation of optimal control trajectories associated with a class of nonlinear…

We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of…

Several studies have shown the ability of natural gradient descent to minimize the objective function more efficiently than ordinary gradient descent based methods. However, the bottleneck of this approach for training deep neural networks…

We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the…