相关论文: Trajectory Optimization by Successive Pseudospectr…

This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…

The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant…

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…

This research addresses the increasing demand for advanced navigation systems capable of operating within confined surroundings. A significant challenge in this field is developing an efficient planning framework that can generalize across…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…

Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…

This paper reports the design of a high-accuracy spatial location estimation method using ultrasound waves by exploiting the fixed geometry of the transmitters. Assuming an isosceles triangle antenna configuration, where three antennas are…

The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used.…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

This paper addresses the challenge of accommodating nonlinear dynamics and constraints in rapid trajectory optimization, envisioned for use in the context of onboard guidance. We present a novel framework that uniquely employs…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

In this paper, we propose a Riemannian smoothing steepest descent method to minimize a nonconvex and non-Lipschitz function on submanifolds. The generalized subdifferentials on Riemannian manifold and the Riemannian gradient sub-consistency…

Riemannian accelerated gradient methods have been well studied for smooth optimization, typically treating geodesically convex and geodesically strongly convex cases separately. However, their extension to nonsmooth problems on manifolds…

This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…

This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

We propose a nonlinear model predictive control (NMPC) framework based on a direct optimal control method that ensures continuous-time constraint satisfaction and accurate evaluation of the running cost, without compromising computational…

We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…