Convex matrix optimization problem

Can augmented Lagrangian methods solve convex matrix optimization problems?

Under a mild quadratic growth condition on the dual of cMOP, we further discussed the R-superlinear convergence of the Karush–Kuhn–Tucker (KKT) residuals of the sequence generated by the augmented Lagrangian methods (ALM) for solving convex matrix optimization problems

How do you find a convex matrices?

xT (θA + (1 − θ)B)x = θxT Ax + (1 − θ)xT Bx ≥ 0

The same logic can be used to show that the sets of all positive definite, negative definite, and negative semidefinite matrices are each also convex

central element in convex optimization is the notion of a convex function f(θx + (1 − θ)y) ≤ θf(x) + (1 − θ)f(y)

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