相关论文: Model-Free Optimization on Smooth Compact Manifold…

We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean…

We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments containing obstacles, with arbitrary non-convex shapes, which can be in close proximity with each other, as long as there exists at least…

We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{\L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive…

Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…

Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited…

A novel derivative-free algorithm, optimization by moving ridge functions (OMoRF), for unconstrained and bound-constrained optimization is presented. This algorithm couples trust region methodologies with output-based dimension reduction to…

This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization…

This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\'echet or G\^ateaux…

We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…

Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…

Multiscale topology optimization is crucial for designing porous infill structures with high stiffness-to-weight ratios and excellent energy absorption. Although gradient-based methods provide a rigorous framework, they are computationally…

Topology optimization (TO) has experienced a dramatic development over the last decades aided by the arising of metamaterials and additive manufacturing (AM) techniques, and it is intended to achieve the current and future challenges. In…

We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…

Compatible schemes localize degrees of freedom according to the physical nature of the underlying fields and operate a clear distinction between topological laws and closure relations. For elliptic problems, the cornerstone in the scheme…

We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…

This article aims to provide an accessible, tutorial-style introduction to hybrid extremum-seeking systems, which are model-free, feedback-optimization controllers that incorporate hybrid dynamics, meaning both continuous-time and…

We introduce a new hybrid control strategy, which is conceptually different from the commonly used synergistic hybrid approaches, to efficiently deal with the problem of the undesired equilibria that precludes smooth vectors fields on…

In this paper, we present a novel control framework to achieve robust push recovery on bipedal robots while locomoting. The key contribution is the unification of hybrid system models of locomotion with a reduced-order model predictive…

In this work, we focus on the study of stochastic zeroth-order (ZO) optimization which does not require first-order gradient information and uses only function evaluations. The problem of ZO optimization has emerged in many recent machine…

Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability…