A penalty function method approach is proposed to solve the general problem of quotient space norms minimization. A new class of penalty functions is introduced which allows one to transform constrained optimization problems of quotient space norms minimization by unconstrained optimization problems. The sharp bound on the weight parameter is given for which constrained and unconstrained problems are equivalent. Also a computationally efficient bound on the weight parameter is given. Numerical examples and computer simulations illustrate the results obtained.
Minimum norm problems, Constrained optimization, Penalty method, Linear equations. AMS Subject Classification: 15A60, 15A06, 34A30, 90C30
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