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This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$…
In this paper we address the speed planning problem for a vehicle along a predefined path. A weighted average of two (conflicting) terms, energy consumption and travel time, is minimized. After deriving a non-convex mathematical model of…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
This paper studies the long-time behavior of optimal solutions for a class of linear-convex optimal control problems. We focus on a partial exponential turnpike property, established without imposing controllability or stabilizability…
In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of…
This paper studies the time-optimal path tracking problem for a team of cooperating robotic manipulators carrying an object. Considering the problem for rigidly grasped objects, we show that it can be cast as a convex optimization problem…
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
We consider an obstacle problem for (possibly non-local) wave equations, and we prove existence of weak solutions through a convex minimization approach based on a time discrete approximation scheme. We provide the corresponding numerical…
This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
We establish the boundedness of time derivatives of solutions to parabolic $p$-Laplace equations. Our approach relies on the Bernstein technique combined with a suitable approximation method. As a consequence, we obtain an optimal…
This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear terms that satisfy global Lipschitz conditions. It is shown…
A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable discretization of the nonlinear inextensibility constraint.…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex…
We derive existence results and first order necessary optimality conditions for optimal control problems governed by quasilinear parabolic PDEs with a class of first order nonlinearities that include for instance quadratic gradient terms.…
Most interesting problems in robotics (e.g., locomotion and manipulation) are realized through intermittent contact with the environment. Due to the perception and modeling errors, assuming an exact time for establishing contact with the…
The paper focuses on a multidimensional optimization problem, which is formulated in terms of tropical mathematics and consists in minimizing a nonlinear objective function subject to linear inequality constraints. To solve the problem, we…