Summary
This paper presents a readily implementable algorithm for solving constrained minimization problems involving (possibly nonsmooth) convex functions. The constraints are handled as in the successive quadratic approximations methods for smooth problems. An exact penalty function is employed for stepsize selection. A scheme for automatic limitation of penalty growth is given. Global convergence of the algorithm is established, as well as finite termination for piecewise linear problems. Numerical experience is reported.
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Kiwiel, K.C. A constraint linearization method for nondifferentiable convex minimization. Numer. Math. 51, 395–414 (1987). https://doi.org/10.1007/BF01397543
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DOI: https://doi.org/10.1007/BF01397543