arXiv subjects

Du Zou

Publications and source records attributed to Du Zou.

4 recordsLinked to original sources

arXiv2024

Open-loop Pareto-Nash equilibria in multi-objective interval differential games

The paper explores n-player multi-objective interval differential games, where the terminal payoff function and integral payoff function of players are both interval-vector-valued functions. Firstly, by leveraging the partial order relationship among interval vectors, we establish the concept of (weighted) open-loop Pareto-Nash equilibrium for multi-objective interval differential games and derive two theorems regarding the existence of such equilibria. Secondly, necessary conditions for open-loop Pareto-Nash equilibria in n-player interval differential games are derived through constructing Hamilton functions in an interval form and applying the Pontryagin maximum principle. Subsequently, sufficient conditions for their existence are provided by defining a maximization Hamilton function and utilizing its concavity. Finally, a two-player linear quadratic interval differential game is discussed along with a specific calculation method to determine its open-loop Pareto-Nash equilibrium.

math.OC↗

arXiv2017

Lp Minkowski problem for electrostatic $\mathfrak{p}$-capacity

Existence and uniqueness of the solution to the discrete Lp Minkowski problem for $\mathfrak{p}$-capacity are proved when $p \geq 1$ and $1<\mathfrak{p}<n$. For general Lp Minkowski problem for $\mathfrak{p}$-capacity, existence and uniqueness of the solution are given when $p \geq 1$ and $1<\mathfrak{p}\le 2$. These results are non-linear extensions of the very recent solution to the Lp Minkowski problem for $\mathfrak{p}$-capacity when $p=1$ and $1<\mathfrak{p}\le n$ by CNSXYZ, and the classical soution to the Minkowski problem for electrostatic capacity when $p=1$ and $\mathfrak{p}=2$ by Jerison.

math.DG↗

arXiv2016

A unified treatment for Lp Brunn-Minkowski type inequalities

A unified approach used to generalize classical Brunn-Minkowski type inequalities to Lp Brunn-Minkowski type inequalities, called the Lp transference principle, is refined in this paper. As illustrations of the effectiveness and practicability of this method, several new Lp Brunn-Minkowski type inequalities concerning the mixed volume, moment of inertia, quermassintegral, projection body and capacity are established.

math.MG↗

arXiv2014

Orlicz-Legendre Ellipsoids

The Orlicz-Legendre ellipsoids, which are in the framework of emerging dual Orlicz Brunn-Minkowski theory, are introduced for the first time. They are in some sense dual to the recently found Orlicz-John ellipsoids, and have largely generalized the classical Legendre ellipsoid of inertia. Several new affine isoperimetric inequalities are established. The connection between the characterization of Orlicz-Legendre ellipsoids and isotropy of measures is demonstrated.

math.MG↗