Convex optimization medium

Convex functions are important in optimization because local minima of a convex function is also a global minima.
Therefore, once we find a local minima, our minimization problem is solved and we have found minimum loss._{Mar 5, 2022}

Convex optimization involves minimizing convex functions over convex sets. Convex functions and sets have helpful mathematical properties that make these problems well-suited for efficient optimization algorithms. Specifically, local optima are guaranteed to be global optima for convex problems.

What are the requirements for convex optimization?

Comparing (4 15) with the general standard form problem (4

1), the convex problem has three additional requirements: 4

2 Convex optimization 137 • the objective function must be convex, • the inequality constraint functions must be convex, • the equality constraint functions hi(x) = aT ix−bimust be aﬃne

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