Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Mathematical Programming: Series A and B
Warm start of the primal-dual method applied in the cutting-plane scheme
Mathematical Programming: Series A and B
Warm-Start Strategies in Interior-Point Methods for Linear Programming
SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Mathematical Programming: Series A and B
Computational Optimization and Applications
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
An entire space polynomial-time algorithm for linear programming
Journal of Global Optimization
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In this paper, primal-dual methods for general nonconvex nonlinear optimization problems are considered. The proposed methods are exterior point type methods that permit primal variables to violate inequality constraints during the iterations. The methods are based on the exact penalty type transformation of inequality constraints and use a smooth approximation of the problem to form primal-dual iteration based on Newton's method as in usual primal-dual interior point methods. Global convergence and local superlinear/quadratic convergence of the proposed methods are proved. For global convergence, methods using line searches and trust region type searches are proposed. The trust region type method is tested with CUTEr problems and is shown to have similar efficiency to the primal-dual interior point method code IPOPT. It is also shown that the methods can be warm started easily, unlike interior point methods, and that the methods can be efficiently used in parametric programming problems.