Results 61 to 70 of about 638 (183)

“It Is Much Safer to Be Sparse than Connected”: Safe Control of Robotic Swarm Density Dynamics with PDE Optimization with State Constraints

Advanced Intelligent Systems, Volume 8, Issue 7, July 2026.
This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
wiley   +1 more source

Economic Growth and the Rise of Large Firms

Econometrica, Volume 94, Issue 4, Page 1375-1408, July 2026.
I document that the right tail of the firm size distribution systematically thickens with economic development. To rationalize this fact, I develop a parsimonious idea search model in which both aggregate growth and the firm size distribution are endogenously determined.
Zhang Chen
wiley   +1 more source

ON THE STRUCTURE OF THE SINGULAR SET OF A PIECEWISE SMOOTH MINIMAX SOLUTION OF THE HAMILTON–JACOBI–BELLMAN EQUATION

Ural Mathematical Journal, 2016
The properties of a minimax piecewise smooth solution of the Hamilton–Jacobi–Bellman equation are studied. It is known the Rankine–Hugoniot conditions are necessary and sufficient conditions for the points of nondifferentiability (singularity) of the ...
Aleksei S. Rodin
doaj   +1 more source

Improved patchy solution to the Hamilton-Jacobi-Bellman equations [PDF]

49th IEEE Conference on Decision and Control (CDC), 2010
We test a new patch type for the patchy approximate solution to the Hamilton-Jacobi-Bellman equations, and we see an improvement in the worst relative error on a nonlinear test problem.
Hunt, Thomas, Krener, Arthur J.
openaire   +2 more sources

Three reasons to price carbon under uncertainty: Accuracy of simple rules

Quantitative Economics, Volume 17, Issue 3, Page 858-894, July 2026.
An easy‐to‐interpret rule for the optimal risk‐adjusted social cost of carbon is derived using perturbation analysis. This rule internalizes the adverse effects of global warming on the risk of recurring climate‐related disasters, the risk of irreversible cascading climate tipping points, and the usual effect on total factor productivity.
Ton van den Bremer, Christoph Hambel, Frederick van der Ploeg   +2 more
wiley   +1 more source

Model Ambiguity versus Model Misspecification in Dynamic Portfolio Choice

The Journal of Finance, Volume 81, Issue 3, Page 1741-1795, June 2026.
ABSTRACT We study aversion to model ambiguity and misspecification in dynamic portfolio choice. Risk‐averse investors (relative risk aversion γ>1$\gamma > 1$) fear return persistence, while risk‐tolerant investors (0<γ<1$0<\gamma <1$) fear mean reversion, when confronting model misspecification concerns of identically and independently distributed (IID)
PASCAL J. MAENHOUT, HAO XING, ANNE G. BALTER   +2 more
wiley   +1 more source

A Semi-Lagrangian Scheme for Hamilton--Jacobi--Bellman Equations on Networks

SIAM Journal on Numerical Analysis, 2020
The authors discuss the numerical solution of a Hamilton-Jacobi-Bellmann (HJB) equation. A semi-Lagrangian scheme is proposed and basic properties of this scheme, as e.g., monotonicity, stability, almost Lipschitz regularity, and consistency are shown. The convergence of the approximate solution to the exact solution of the HJB equation is proved.
Elisabetta Carlini, Adriano Festa, Nicolas Forcadel   +2 more
openaire   +2 more sources

Direct Numerical Simulation of Magnetohydrodynamic Slip‐Flow Past a Stretching Surface Using Physics‐Informed Neural Network

Heat Transfer, Volume 55, Issue 3, Page 1674-1682, May 2026.
ABSTRACT Traditional numerical methods, such as finite difference methods (FDM), finite element methods (FEM), and spectral methods, often face meshing challenges and high computational cost for solving nonlinear coupled differential equations. Machine learning techniques, specifically Physics‐informed machine learning, address these obstacles by ...
Ahmad, Feroz Soomro, Husna Zafar
wiley   +1 more source

Existence of viscosity solutions to abstract Cauchy problems via nonlinear semigroups

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract In this work, we provide conditions for nonlinear monotone semigroups on locally convex vector lattices to give rise to a generalized notion of viscosity solutions to a related nonlinear partial differential equation. The semigroup needs to satisfy a convexity estimate, so called K$K$‐convexity, with respect to another family of operators ...
Fabian Fuchs, Max Nendel
wiley   +1 more source

Stochastic Optimal Control of Averaged SDDE with Semi-Markov Switching and with Application in Economics

Mathematics
This paper is devoted to the study of stochastic optimal control of averaged stochastic differential delay equations (SDDEs) with semi-Markov switchings and their applications in economics.
Mariya Svishchuk, Anatoliy V. Swishchuk
doaj   +1 more source