相关论文: Building Rome with Convex Optimization

We present a constrained motion control framework for a redundant surgical system designed for minimally invasive treatment of pelvic osteolysis. The framework comprises a kinematics model of a six Degrees-of-Freedom (DoF) robotic arm…

In this paper, we propose an interior-point method for linearly constrained optimization problems (possibly nonconvex). The method - which we call the Hessian barrier algorithm (HBA) - combines a forward Euler discretization of Hessian…

Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a…

Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…

We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by…

In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…

This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…

Proximal bundle methods (PBM) are a powerful class of algorithms for convex optimization. Compared to gradient descent, PBM constructs more accurate surrogate models that incorporate gradients and function values from multiple past…

Visualizing graphs using virtual physical models is probably the most heavily used technique for drawing graphs in practice. There are many algorithms that are efficient and produce high-quality layouts. If one requires that the layout also…

Group synchronization aims to recover the group elements from their noisy pairwise measurements. It has found many applications in community detection, clock synchronization, and joint alignment problem. This paper focuses on the orthogonal…

The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving nonsmooth optimization problems. In this paper, we present the first variant of the PBM for smooth objectives, achieving an accelerated…

This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…

We develop model-based methods for solving stochastic convex optimization problems, introducing the approximate-proximal point, or aProx, family, which includes stochastic subgradient, proximal point, and bundle methods. When the modeling…

Optimization on Hadamard manifolds -- the natural Riemannian setting for globally geodesically convex problems -- relies on exponential maps to retract tangent vectors and parallel transport to connect tangent spaces across the manifold.…

Recent advances in the efficiency and robustness of algorithms solving convex quadratically constrained quadratic programming (QCQP) problems motivate developing techniques for creating convex quadratic relaxations that, although more…

We propose a structural default model for portfolio-wide valuation adjustments (xVAs) and represent it as a system of coupled backward stochastic differential equations. The framework is divided into four layers, each capturing a key…

This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are batch methods designed mainly based on the convex optimization, say, the…

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…