Related papers: Optimization and variational principles for the sh…
We present a method for finding lower bounds on the global infima of integral variational problems, wherein $\int_\Omega f(x,u(x),\nabla u(x)){\rm d}x$ is minimized over functions $u\colon\Omega\subset\mathbb{R}^n\to\mathbb{R}^m$ satisfying…
High-level penetration of intermittent renewable energy sources (RESs) has introduced significant uncertainties into modern power systems. In order to rapidly and economically respond to the fluctuations of power system operating state,…
The low-rank stochastic semidefinite optimization has attracted rising attention due to its wide range of applications. The nonconvex reformulation based on the low-rank factorization, significantly improves the computational efficiency but…
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…
Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…
This paper presents consideration of the Semi-Relaxed Sinkhorn (SR-Sinkhorn) algorithm for the semi-relaxed optimal transport (SROT) problem, which relaxes one marginal constraint of the standard OT problem. For evaluation of how the…
Constrained combinatorial optimization problems (CCOPs) are challenging to solve due to the exponential growth of the solution space. When tackled with Ising machines, constraints are typically enforced by the penalty function method, whose…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
Variance reduction techniques are popular in accelerating gradient descent and stochastic gradient descent for optimization problems defined on both Euclidean space and Riemannian manifold. In this paper, we further improve on existing…
Stochastic proximal point methods have recently garnered renewed attention within the optimization community, primarily due to their desirable theoretical properties. Notably, these methods exhibit a convergence rate that is independent of…
Stochastic variance reduction has proven effective at accelerating first-order algorithms for solving convex finite-sum optimization tasks such as empirical risk minimization. Incorporating second-order information has proven helpful in…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We formulate a novel numerical method suitable for the solution of topology optimization problems in solid mechanics. The most salient feature of the new approach is that the space and time discrete equations of the numerical method can be…
In this paper, we develop a robust efficient visual SLAM system that utilizes heterogeneous point and line features. By leveraging ORB-SLAM [1], the proposed system consists of stereo matching, frame tracking, local mapping, loop detection,…
Many optimization problems incorporate uncertainty affecting their parameters and thus their objective functions and constraints. As an example, in chance-constrained optimization the constraints need to be satisfied with a certain…
Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…