Penalty and Barrier Methods

David G. Luenberger and Yinyu Ye
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David G. Luenberger: Stanford University
Yinyu Ye: Stanford University

Chapter Chapter 13 in Linear and Nonlinear Programming, 2021, pp 455-486 from Springer

Abstract: Abstract Penalty and barrier methods are procedures for approximating constrained optimization problems by unconstrained problems. The approximation is accomplished in the case of penalty methods by adding to the objective function a term that prescribes a high cost for violation of the constraints, and in the case of barrier methods by adding a term that favors points interior to the feasible region over those near the boundary. Associated with these methods is a parameter c or μ that determines the severity of the penalty or barrier and consequently the degree to which the unconstrained problem approximates the original constrained problem. For a problem with n variables and m constraints, penalty and barrier methods work directly in the n-dimensional space of variables, as compared to primal methods that work in (n − m)-dimensional space.

Date: 2021
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DOI: 10.1007/978-3-030-85450-8_13

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