We consider several non-standard discrete and continuous Green energy problems in the complex plane and study the asymptotic relations between their solutions. In the discrete setting, we consider two problems; one with variable particle positions (within a given compact set) and variable particle masses, the other one with variable masses but prescribed positions. The mass of a particle is allowed to take any value in the range \(0\le m\le R\), where \(R>0\) is a fixed parameter in the problem. The corresponding continuous energy problems are defined on the space of positive measures \(\mu \) with mass \(\Vert \mu \Vert \le R\) and supported on the given compact set, with an additional upper constraint that appears as a consequence of the prescribed positions condition. It is proved that the equilibrium constant and equilibrium measure vary continuously as functions of the parameter R (the latter in the weak-star topology). In the unconstrained energy problem we present a greedy algorithm that converges to the equilibrium constant and equilibrium measure. In the discrete energy problems, it is shown that under certain conditions, the optimal values of the particle masses are uniquely determined by the optimal positions or prescribed positions of the particles, depending on the type of problem considered.

我们在复平面上考虑几个非标准离散和连续绿色能源问题，并研究它们的解之间的渐近关系。在离散设置中，我们考虑两个问题；一种具有可变的粒子位置（在给定的紧凑集合内）和可变的粒子质量，另一种具有可变的质量但规定的位置。粒子的质量允许取\(0\le m\le R\)范围内的任何值，其中\(R>0\)是问题中的固定参数。相应的连续能量问题定义在质量为\(\Vert \mu \Vert \le R\ )的正测度空间\(\mu \) 上并在给定的紧凑集上受到支持，并具有作为规定位置条件的结果而出现的附加上限约束。证明了平衡常数和平衡测度作为参数R（弱星形拓扑中的后者）的函数连续变化。在无约束能量问题中，我们提出了一种收敛于平衡常数和平衡测度的贪心算法。在离散能量问题中，表明在某些条件下，粒子质量的最佳值由粒子的最佳位置或规定位置唯一确定，具体取决于所考虑问题的类型。