saddle point of lagrange function (interpretation)

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How to interpret tha following definition for non-linear programming? The triplet $(x^{1},u^{1},v^{1})$ is called a saddle point of Lagrange function $L$ on the region $M\times\mathbb{R}^{J}_{+}\times\mathbb{R}^{K}$ if $$ L(x^{1},u,v)\le L(x^{1},u^{1},v^{1})\le L(x,u^{1},v^{1}),\quad \forall x\in M,u\in \mathbb{R}^{J}_{+},v\in \mathbb{R}^{K} $$