Related papers: Trajectory Optimization on Manifolds: A Theoretica…

To be applicable to real world scenarios trajectory planning schemes for mobile autonomous systems must be able to efficiently deal with obstacles in the area of operation. In the context of optimization based trajectory planning and…

We consider a class of (possibly strongly) geodesically convex optimization problems on Hadamard manifolds, where the objective function splits into the sum of a smooth and a possibly nonsmooth function. We introduce an intrinsic convex…

Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…

Vehicle trajectory optimization is essential to ensure vehicles travel efficiently and safely. This paper presents an infrastructure assisted constrained connected automated vehicles (CAVs) trajectory optimization method on curved roads.…

We introduce an algorithm called SQDP (Stochastic Quadratic Dynamic Programming) to solve some multistage stochastic optimization problems having strongly convex recourse functions. The algorithm extends the classical Stochastic Dual…

A typical manipulation task consists of a manipulator equipped with a gripper to grasp and move an object with constraints on the motion of the hand-held object, which may be due to the nature of the task itself or from object-environment…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

Machine learning (ML) approaches are increasingly being used to accelerate combinatorial optimization (CO) problems. We investigate the Set Cover Problem (SCP) and propose Graph-SCP, a graph neural network method that augments existing…

The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning,…

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

In recent times, an increasing number of researchers have been devoted to utilizing deep neural networks for end-to-end flight navigation. This approach has gained traction due to its ability to bridge the gap between perception and…

Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and optimizing control policies on these manifolds is a fundamental problem. In this work, we propose a novel computationally efficient approach…

Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…

Efficient performance of a number of engineering systems is achieved through different modes of operation - yielding systems described as "hybrid", containing both real-valued and discrete decision variables. Prominent examples of such…

Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…

We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…

This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…

In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…

This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the…