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A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
In this paper, we study the stability and convergence of continuous-time Lagrangian saddle flows to solutions of a convex constrained optimization problem. Convergence of these flows is well-known when the underlying saddle function is…
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic…
In this paper, we proposed an alternating projection based algorithm to solve a class of distributed MIN-MAX convex optimization problems. We firstly transform this MINMAX problem into the problem of searching for the minimum distance…
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…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…
This paper presents a novel feedback method on the motion planning for unicycle robots in environments with static obstacles, along with an extension to the distributed planning and coordination in multi-robot systems. The method employs a…
A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
We consider the problem of cooperative intersection management. It arises in automated transportation systems for people or goods but also in multi-robots environment. Therefore many solutions have been proposed to avoid collisions. The…
Real-time kinodynamic trajectory planning in dynamic environments is critical yet challenging for autonomous driving. In this letter, we propose an efficient trajectory planning system for autonomous driving in complex dynamic scenarios…
We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape…
We give an algorithm to compute a morph between any two convex drawings of the same plane graph. The morph preserves the convexity of the drawing at any time instant and moves each vertex along a piecewise linear curve with linear…
Diffusion and flow-matching have emerged as powerful methodologies for generative modeling, with remarkable success in capturing complex data distributions and enabling flexible guidance at inference time. Many downstream applications,…
This work examines the conditions for asymptotic and exponential convergence of saddle flow dynamics of convex-concave functions. First, we propose an observability-based certificate for asymptotic convergence, directly bridging the gap…
In this paper, we study the problem of optimal multi-robot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions…
We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control,…
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by…