Related papers: Trajectory Optimization on Manifolds: A Theoretica…

We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a…

In this paper we study a broad class of structured nonlinear programming (SNLP) problems. In particular, we first establish the first-order optimality conditions for them. Then we propose sequential convex programming (SCP) methods for…

In this paper, we study the sequential convex programming method with monotone line search (SCP$_{ls}$) in [46] for a class of difference-of-convex (DC) optimization problems with multiple smooth inequality constraints. The SCP$_{ls}$ is a…

This work investigates the challenge of ensuring safety guarantees in the presence of uncontrollable agents, whose behaviors are stochastic and depend on both their own and the system's states. We present a neural model predictive control…

Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…

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,…

We study a class of constrained nonconvex-nonconcave minimax optimization problems in which the inner maximization involves potentially complex constraints. Under the assumption that the inner problem of a novel lifted minimax reformulation…

We propose a data-driven Model Predictive Control (MPC) framework that employs a transformer encoder to generate multi-step predictions. To handle the nonconvex attention mechanism, we derive difference of convex (DC) representations of the…

We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…

This article explores an approach to addressing the Close Enough Traveling Salesman Problem (CETSP). The objective is to streamline the mathematical formulation by introducing reformulations that approximate the Euclidean distances and…

Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…

We introduce a multi-phase rocket landing guidance framework that can handle nonlinear dynamics and does not mandate any additional mixed-integer or nonconvex constraints to handle discrete temporal events/switching. To achieve this, we…

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…

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…

The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…

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…

This paper presents a spatial-based trajectory planning method for automated vehicles under actuator, obstacle avoidance, and vehicle dimension constraints. Starting from a nonlinear kinematic bicycle model, vehicle dynamics are transformed…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

Smooth convex minimization over the unit trace-norm ball is an important optimization problem in machine learning, signal processing, statistics and other fields, that underlies many tasks in which one wishes to recover a low-rank matrix…

Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…