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A. multi-dimensional state, one-dimensional time Multi-dimensional extensions $x\in\mathbb{R}^n$ of the one-dimensional Hamilton-Jacobi-Bellman equations have been considered in Consistency of a Simp …

Maximum Mass of a Neutron Star (1974) Control theory and singular Riemannian geometry (1982) The Condition of Hydrostatic Equilibrium of Stellar Models Using Optimal Control (2002) Investigating a …

You could use the Gershgorin circle theorem. For an $n\times n$ matrix $M$, consider $n$ circles $C_i$, $i=1,2,\ldots n$ in the complex plane centered at $M_{ii}$, with radius $\sum_{j\neq i}|M_{ij}|$ …

"Calculus of variations" seems an accepted umbrella term; at least, looking at the corresponding Wikipedia entry, you'll recognize that most problems in this class are of the type you are looking for: …

This is the earliest reference I have located: Minkowski-Farkas Lemma in Banach Spaces, L. Hurwicz (1952). The same result was also referred to as the Minkowski-Farkas-Weyl theorem in the 1950's, for …

This web site provides a good entry point on Kalman filtering. It has a listing of books, software and more. The applications are biased towards navigation, but the applications to economic time serie …

A way to approach your problem could be to consider the calculation of the expectation value as a Monte Carlo integration. Then you can use established techniques of variance reduction, as described f …

Inverse Problems for Partial Differential Equations (third edition, 2017) by Victor Isakov concludes each chapter with a collection of open research problems. Chapter 9 is specifically devoted to inve …

The 2022 article A Gradient-Based Implementation of the Polyhedral Active Set Algorithm discusses one particular PASA implementation in much detail --- it does not seem to require much by way of backg …

The lecture notes on mean-field games of Lions, from a course at the Collège de France, have been typed out by Pierre Cardaliaguet. They address both optimal control and dynamic programming. I would t …

There are two principles at play here: a mathematical principle that favors hexagonal networks, and a physical principle that favors a network with straight walls. The mathematical principle that pref …

Edit: An earlier version of this answer missed a factor of two, now corrected, thanks to Daniele Tampieri. We seek the variation of the functional $$L[u]=\int_\Omega\left(|\nabla u|^2+1\right)\chi_{u> …