Related papers: Existence and optimality of strong stability prese…
In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is often preferred. On the other…
We prove existence and uniqueness of strong solutions, as well as continuous dependence on the initial datum, for a class of fully nonlinear second-order stochastic PDEs with drift in divergence form. Due to rather general assumptions on…
We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our…
High order strong stability preserving (SSP) time discretizations ensure the nonlinear non-inner-product strong stability properties of spatial discretizations suited for the stable simulation of hyperbolic PDEs. Over the past decade…
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in…
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…
In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
This article concerns the stability of a model for mass-spring systems with positive damping and negative stiness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the…
Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…
This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete…
In this paper, we introduce a linear stochastic volatility model driven by $\alpha$-stable processes, which admits a unique positive solution. To preserve positivity, we modify the classical forward Euler-Maruyama scheme and analyze its…
Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic…
Numerical analysis for linear constant-coefficients Finite Difference schemes was developed approximately fifty years ago. It relies on the assumption of scheme stability and in particular -- for the $L^2$ setting -- on the absence of…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- in which for each…
This work assesses both empirically and theoretically, using the performance estimation methodology, how robust different first-order optimization methods are when subject to relative inexactness in their gradient computations. Relative…
This paper studies bipedal locomotion as a nonlinear optimization problem based on continuous and discrete dynamics, by simultaneously optimizing the remaining step duration, the next step duration and the foot location to achieve…
We provide new results on the existence of nonzero positive weak solutions for a class of second order elliptic systems. Our approach relies on a combined use of iterative techniques and classical fixed point index. Some examples are…