Related papers: Convergence rate analysis and improved iterations …
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…
This paper addresses the numerical computation of critical angles between two convex cones in finite-dimensional Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary…
Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
We survey recent work on machine learning (ML) techniques for selecting cutting planes (or cuts) in mixed-integer linear programming (MILP). Despite the availability of various classes of cuts, the task of choosing a set of cuts to add to…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
There is an increasing interest in quantum algorithms for optimization problems. Within convex optimization, interior-point methods and other recently proposed quantum algorithms are non-trivial to implement on noisy quantum devices. Here,…
Projective splitting is a family of methods for solving inclusions involving sums of maximal monotone operators. First introduced by Eckstein and Svaiter in 2008, these methods have enjoyed significant innovation in recent years, becoming…
A novel algorithm for the computation of the quadratic numerical range is presented and exemplified yielding much better results in less time compared to the random vector sampling method. Furthermore, a bound on the probability for the…
Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental…
This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…
We propose a multi-precision extension of the Quadratic Regularization (R2) algorithm that enables it to take advantage of low-precision computations, and by extension to decrease energy consumption during the solve. The lower the precision…
This paper proposes a novel class of block quasi-Newton methods for convex optimization which we call symmetric rank-$k$ (SR-$k$) methods. Each iteration of SR-$k$ incorporates the curvature information with~$k$ Hessian-vector products…
This paper presents a comprehensive analysis of the well-known extragradient (EG) method for solving both equations and inclusions. First, we unify and generalize EG for [non]linear equations to a wider class of algorithms, encompassing…
A numerical algorithm for mean curvature flow of closed mean convex surfaces with surgery is proposed. The method uses a finite element based mean curvature flow algorithm based on a coupled partial differential equation system which…
Iterative methods with certified convergence for the computation of Gauss--Jacobi quadratures are described. The methods do not require a priori estimations of the nodes to guarantee its fourth-order convergence. They are shown to be…
In this work, we study the iteration complexity of gradient methods for minimizing convex quadratic functions regularized by powers of Euclidean norms. We show that, due to the uniform convexity of the objective, gradient methods have…
Optimization is important in machine learning problems, and quasi-Newton methods have a reputation as the most efficient numerical schemes for smooth unconstrained optimization. In this paper, we consider the explicit superlinear…
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…
Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of…