dilettagoglia / unconstrained-optimization

Estimating the 2-norm for a rectangular matrix (unconstrained approach) using two optimization algorithms: Standard gradient descent (steepest descent) method, and quasi-Newton method

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unconstrained-optimization sgd gradient-descent quasi-newton optimization optimization-algorithms 2-norm algorithms

Unconstrained optimization algorithms

(Problem) is the problem of estimating the matrix norm $||A||_2$ for a (possibly rectangular) matrix $A \in R^{m \times n}$ , using its definition as an (unconstrained) maximum problem.

(Alg1) is a standard gradient descent (steepest descent) approach.

(Alg2) is a a quasi-Newton method such as BFGS (one which does not require any approximations of the Hessian of the function)

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Estimating the 2-norm for a rectangular matrix (unconstrained approach) using two optimization algorithms: Standard gradient descent (steepest descent) method, and quasi-Newton method

unconstrained-optimization sgd gradient-descent quasi-newton optimization optimization-algorithms 2-norm algorithms

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