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From page 4 of this paper by Mengyu Liu & Yuan Liu:

We first introduce non-negative Lagrangian multipliers $\lambda = \{\lambda_k\} \succeq 0$ and $\beta = \{\beta_k\} \succeq 0$ associated with the rate constraint $(15\mathrm d)$, $\nu = \{\nu_k\} \succeq 0$ associated with the energy causality constraints $(15\mathrm e)$ and $(15\mathrm f)$. In addition, non-negative Lagrangian multipliers $\mu \ge 0$ and $\xi \ge 0$ are associated with the total time constraint $(15\mathrm b)$ and total energy constraint at $\mathrm{HRN}$ $(15\mathrm c)$. Then the Lagrangian of Problem $(\mathrm{P1'})$ is given $\cdots$

I found a symbol that I am not familiar with. Does anyone know the symbol $\succeq$?

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    $\preceq$ is generally used to denote an arbitrary partial order or total order where the specific order being referred to is explicitly stated in the context. – JMoravitz Jul 06 '18 at 02:26
  • @Creator "Being majorized by" is an example of a partial order. The specific example that the OP is looking at however does not appear to have anything to do with that partial order specifically, but rather another one. – JMoravitz Jul 06 '18 at 02:33
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    They are writing down the Lagrange dual problem. The symbol $\succcurlyeq$ just means $\geq0$ (for each $k$). See in the dual problem how the dual variables corresponding to inequalities (that 15d are inequality constrains) are imposed the non-negativity condition. –  Jul 06 '18 at 02:33
  • The ${\lambda_k}$ notation is a little unusual. – copper.hat Jul 06 '18 at 02:37
  • Instead of an image of a small portion, a link to the full paper gives more information. –  Jul 06 '18 at 02:37
  • Just to let you know, in Approximation theory, $x \succeq y$ means that there exists a constant $C>0$ independent in $x$, $y$ and some "other parameters" of the context such that $x\geq Cy$ – Gonzalo A. Benavides Jul 06 '18 at 02:56
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    Here's the same question answered elsewhere. Cheers! – Ayo Jul 06 '18 at 02:58
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    @copper.hat In my experience, it is not that unusual. That said, I personally think it is bad notation. – Derek Elkins left SE Jul 06 '18 at 05:01

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