Related papers: A Finsler Geometrical Programming for the Nonlinea…
Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
An urban traffic system is a heterogeneous system, which consists of different types of intersections and dynamics. In this paper, we focus on one type of heterogeneous traffic network, which consists of signalized junctions and…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…
We consider a network equilibrium model (i.e. a combined model), which was proposed as an alternative to the classic four-step approach for travel forecasting in transportation networks. This model can be formulated as a convex minimization…
Within this work, we consider optimization settings for nonlinear, nonstationary fluid-structure interaction. The problem is formulated in a monolithic fashion using the arbitrary Lagrangian-Eulerian framework to set-up the fluid-structure…
In the standard approach to Finsler geometry the metric is defined as a vertical Hessian and the Chern or Cartan connections appear as just two among many possible natural linear connections on the pullback tangent bundle. Here it is shown…
We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints.…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple…
This paper is about generating motion plans for high degree-of-freedom systems that account for collisions along the entire body. A particular class of mathematical programs with complementarity constraints become useful in this regard.…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
In this paper, we introduce a class of nonlinear optimisation problems. Under mild assumptions, we obtain the existence of potential functions and show that the potential function is a generalised solution of a Monge-Amp\`ere type equation.…
Trajectory optimization is a widely used technique in robot motion planning for letting the dynamics and constraints on the system shape and synthesize complex behaviors. Several previous works have shown its benefits in high-dimensional…
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…