相关论文: No-gap second-order optimality conditions for addi…

Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…

This work presents new sufficient conditions for the absence of a gap corresponding to Young measure and occupation measure relaxations for constrained optimal control problems. Unlike existing conditions, these sufficient conditions do not…

Recently, a new local optimality concept for minimax problems, termed calm local minimax points, has been introduced. In this paper, we extend this concept to a general class of nonsmooth, nonconvex nonconcave minimax problems with coupled…

Optimal control problems with discrete-valued inputs are inherently challenging due to their mixed-integer nature, rendering them generally intractable for real-time, safety-critical aerospace applications. Lossless convexification offers a…

While the Pontryagin Maximum Principle can be used to calculate candidate extremals for optimal orbital transfer problems, these candidates cannot be guaranteed to be at least locally optimal unless sufficient optimality conditions are…

The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…

We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\min_x\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly…

In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…

Applying intelligent robot arms in dynamic uncertain environments (i.e., flexible production lines) remains challenging, which requires efficient algorithms for real time trajectory generation. The motion planning problem for robot…

In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly…

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both…

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…

In this paper we study the auxiliary problems that appear in $p$-order tensor methods for unconstrained minimization of convex functions with $\nu$-H\"{o}lder continuous $p$th derivatives. This type of auxiliary problems corresponds to the…

Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and well-studied problem in robotics. In comparison, TOPP subject to…

The paper concerns the study and applications of a new class of optimal control problems governed by a perturbed sweeping process of the hysteresis type with control functions acting in both play-and-stop operator and additive…

This paper exemplifies that saturation is an indispensable structure on measure spaces to obtain the existence and characterization of solutions to nonconvex variational problems with integral constraints in Banach spaces and their dual…

This paper develops and analyzes an accelerated proximal descent method for finding stationary points of nonconvex composite optimization problems. The objective function is of the form $f+h$ where $h$ is a proper closed convex function,…

In this paper, we study a general optimization model, which covers a large class of existing models for many applications in imaging sciences. To solve the resulting possibly nonconvex, nonsmooth and non-Lipschitz optimization problem, we…

This paper proposes a topology optimization method that considers the geometric constraint of no closed cavities to improve the effectiveness of additive manufacturing based on the fictitious physical model approach. First, the basic…