A new polynomial-time algorithm for linear programming
Combinatorica
Mathematical Programming: Series A and B
On the convegence of a sequential penalty function method for constrained minimization
SIAM Journal on Numerical Analysis
Numerical stability and efficiency of penalty algorithms
SIAM Journal on Numerical Analysis
Primal-dual interior-point methods
Primal-dual interior-point methods
Superlinear Convergence of an Interior-Point Method Despite Dependent Constraints
Mathematics of Operations Research
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
High-order Newton-penalty algorithms
Journal of Computational and Applied Mathematics
High-order Newton-penalty algorithms
Journal of Computational and Applied Mathematics
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Since the pioneering work of Karmarkar, much interest was directed to penalty algorithms, in particular to the log barrier algorithm. We analyze in this paper the asymptotic convergence rate of a barrier algorithm when applied to non-linear programs. More specifically, we consider a variant of the SUMT method, in which so called extrapolation predictor steps allowing reducing the penalty parameter r_{k +1}\,{ are followed by some Newton correction steps. While obviously related to predictor-corrector interior point methods, the spirit differs since our point of view is biased toward nonlinear barrier algorithms; we contrast in details both points of view. In our context, we identify an asymptotically optimal strategy for reducing the penalty parameter r and show that if r_{k+1}=r^\alpha_k with α average superlinear convergence order (∼1.1696). Therefore, our main result is to characterize the best possible convergence order for SUMT type methods.