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Then we can write problem (3) as min_{x gamma)} Vert Ex-f Vert _{2}.
We begin to write problem (1.12) in its equivalent integral form.
Note that to write problem (46) in the SOCP form (47), we first took the square root of the objective function of (46).
In order to proceed let's write problem (11) as the following equivalent problem x ^ = minimize x ∑ m = 1 M γ m ( x T x - 2 c m T x + b m ) 2 (12).
First, we write Problem (18) in the form of a minimization program begin{aligned}&!!!min limits _{p=(p_{1},ldots,p_{K)}}left{ f(p):=-sum limits _{n=1}^{N}omega _{n}R_{n}:sum limits _{k=1}^{K}p_{k}^{n}le P_{n};forall n;right.
We can easily write problem (1) in its primal-dual formulation through Fenchel duality [1]: min_{xin X}max_{{v}in V}L x,{v}):=f_{2}(x)+ langle Bx,{v}rangle-f_{1}^({v}), (2) where (Xin R^{N}) and (Vin R^{M}) are two finite-dimensional vector spaces, and (f_{1}^) is the convex conjugate function of (f_{1}) defined as f_{1}^ v =sup_{{omega}in R^{M}}langle{v},{omega}rangle -f_{1}({omega}).
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He used his wide reading in other historical societies and his knowledge of social science to write problem-based history through asking fundamental questions about the structure of Roman society.
While the current state of the art does not provide techniques for making such code accelerators both general and efficient, it is possible and even straightforward to write problem-specific code accelerators, which are simply efficient reimplementations (in a language like Fortran or C) of algorithms stored in an ActivePaper, with the equivalence of the results verified by extensive tests.
We begin by writing problem (1.9) in its equivalent integral form.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com