相关论文: Powered Descent Guidance via First-Order Optimizat…

This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…

In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…

Time-varying optimization problems are prevalent in various engineering fields, and the ability to solve them accurately in real-time is becoming increasingly important. The prediction-correction algorithms used in smooth time-varying…

The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative…

Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…

This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…

These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…

In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an $\epsilon$-stochastic stationary point, where the expected violations of both constraints and…

This paper presents an optimization-based receding horizon trajectory planning algorithm for dynamical systems operating in unstructured and cluttered environments. The proposed approach is a two-step procedure that uses a motion planning…

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

Motivated by applications in machine learning and operations research, we study regret minimization with stochastic first-order oracle feedback in online constrained, and possibly non-smooth, non-convex problems. In this setting, the…

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…

Projected Gradient Descent (PGD) methods offer a simple and scalable approach to topology optimization (TO), yet they often struggle with nonlinear and multi-constraint problems due to the complexity of active-set detection. This paper…

In this paper we analyze several inexact fast augmented Lagrangian methods for solving linearly constrained convex optimization problems. Mainly, our methods rely on the combination of excessive-gap-like smoothing technique developed in…

Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…

This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assuming that the linear span of the dictionary is dense, as in…

In this paper, we present a first-order projection-free method, namely, the universal conditional gradient sliding (UCGS) method, for solving $\varepsilon$-approximate solutions to convex differentiable optimization problems. For objective…

This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…

We propose a novel first-order method for non-convex optimization of the form $\max_{\bm{w}\in\mathbb{R}^d}\mathbb{E}_{\bm{x}\sim\mathcal{D}}[f_{\bm{w}}(\bm{x})]$, termed Progressive Power Homotopy (Prog-PowerHP). The method applies…

Generating locally optimal UAV-trajectories is challenging due to the non-convex constraints of collision avoidance and actuation limits. We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees…