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Penalty/barrier path-following in linearly constrained optimization

Christian Grossmann (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the present paper rather general penalty/barrier path-following methods (e.g. with p-th power penalties, logarithmic barriers, SUMT, exponential penalties) applied to linearly constrained convex optimization problems are studied. In particular, unlike in previous studies [1,11], here simultaneously different types of penalty/barrier embeddings are included. Together with the assumed 2nd order sufficient optimality conditions this required a significant change in proving the local existence of...

Projection method with level control in convex minimization

Robert Dylewski (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study a projection method with level control for nonsmoooth convex minimization problems. We introduce a changeable level parameter to level control. The level estimates the minimal value of the objective function and is updated in each iteration. We analyse the convergence and estimate the efficiency of this method.

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