Solving the cost function optimization problem using linear programming

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My cost function is in the form $$ \Delta u^T P \Delta u + q^T \Delta u$$How shall I put it in the form of $c^T x$ to be able to solve it using linear programming?

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Assume $P$ symmetric positive definit. Then your problem is equivalent to $$ \min 0 $$ subject to $$ P\Delta u + q = 0. $$