相关论文: Shonan Rotation Averaging: Global Optimality by Su…

The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of action…

Phase retrieval (PR) is an inverse problem about recovering a signal from phaseless linear measurements. This problem can be effectively solved by minimizing a nonconvex amplitude-based loss function. However, this loss function is…

In this paper, the partial relaxation approach is introduced and applied to DOA estimation using spectral search. Unlike existing methods like Capon or MUSIC which can be considered as single source approximations of multi-source estimation…

This paper discusses how to find the global minimum of functions that are summations of small polynomials (``small'' means involving a small number of variables). Some sparse sum of squares (SOS) techniques are proposed. We compare their…

This paper proposes a deep recurrent Rotation Averaging Graph Optimizer (RAGO) for Multiple Rotation Averaging (MRA). Conventional optimization-based methods usually fail to produce accurate results due to corrupted and noisy relative…

Semi-dual neural optimal transport learns a transport map via a max-min objective, yet training can converge to incorrect or degenerate maps. We fully characterize these spurious solutions in the common regime where data concentrate on…

In this paper we propose a real-time and robust solution to large-scale multiple rotation averaging. Until recently, Multiple rotation averaging problem had been solved using conventional iterative optimization algorithms. Such methods…

High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…

This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…

In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk preference parameters. We introduce a perturbation sample…

We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…

There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…

Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in…

Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…

Optimal power flow (OPF) is an important problem in the operation of electric power systems. Due to the OPF problem's non-convexity, there may exist multiple local optima. Certifiably obtaining the global solution is important for certain…

We study regularizations of Schwartz distributions on a complete Riemannian manifold $M$. These approximations are based on families of smoothing operators obtained from the solution operator to the wave equation on $M$ derived from the…

Synchronization of rotations is the problem of estimating a set of rotations R_i in SO(n), i = 1, ..., N, based on noisy measurements of relative rotations R_i R_j^T. This fundamental problem has found many recent applications, most…

We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…

We propose Regularized Overestimated Newton (RON), a Newton-type method with low per-iteration cost and strong global and local convergence guarantees for smooth convex optimization. RON interpolates between gradient descent and globally…

We use a rank one Gaussian perturbation to derive a smooth stochastic approximation of the maximum eigenvalue function. We then combine this smoothing result with an optimal smooth stochastic optimization algorithm to produce an efficient…