Related papers: Improvements of the local bosonic algorithm
We consider the minimization problem with the truncated quadratic regularization with gradient operator, which is a nonsmooth and nonconvex problem. We cooperated the classical preconditioned iterations for linear equations into the…
This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
For non-preconditioned Galerkin systems, the condition number grows with the number of elements as well as the quotient of the maximal and the minimal mesh-size. Therefore, reliable and effective numerical computations, in particular on…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
Local search is an effective method for solving large-scale combinatorial optimization problems, and it has made remarkable progress in recent years through several subtle mechanisms. In this paper, we found two ways to improve the local…
We propose and analyze several schemes for cooling bosonic and fermionic atoms in an optical lattice potential close to the ground state of the no-tunnelling regime. Some of the protocols rely on the concept of algorithmic cooling, which…
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize…
Combinatorial optimization problems can be mapped onto Ising models, and their ground state is generally difficult to find. A lot of heuristics for these problems have been proposed, and one promising approach is to use continuous…
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…
We present a method for improving the speed of geometry relaxation by using a harmonic approximation for the interaction potential between nearest neighbor atoms to construct an initial Hessian estimate. The model is quite robust, and…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…
Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…
Bayesian optimization (BO) is a popular method for optimizing expensive black-box functions. BO has several well-documented shortcomings, including computational slowdown with longer optimization runs, poor suitability for non-stationary or…
In this paper, an improved multimodal optimization (MMO) algorithm,called LSEPSO,has been proposed. LSEPSO combined Electrostatic Particle Swarm Optimization (EPSO) algorithm and a local search method and then made some modification on…
In this paper the approach to solving several combinatorial optimization problems using the local search and the genetic algorithm techniques is proposed. Initially this approach was developed in purpose to overcome some difficulties…
We present a new modified Burg-Like algorithm for spectral estimation and adaptive signal processing, that yield the same prediction coefficients given by the Levinson algorithm for the solution of the normal equations. An equivalency proof…