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Vyacheslav Kungurtsev(vyacheslav.kungurtsevfel.cvut.cz) Abstract: Most pathfollowing algorithms for tracing a solution path of a parametric nonlinear optimization problem are only certifiably convergent under strong regularity assumptions about the problem functions, in particular, the linear independence of the constraint gradients at the solutions, which implies a unique multiplier solution for every nonlinear program. In this paper we propose and prove convergence results for a procedure designed to solve problems satisfying a weaker set of conditions, allowing for nonunique (but bounded) multipliers, applying known sensitivity results for this class of problems. Each iteration along the path consists of three parts: (1) a Newton corrector step for the primal and dual variables, this is obtained by solving a linear system of equations. (2) a tangential predictor step for the primal and dual variables, which is found as the solution of a quadratic programming problem, and (3) a jump step for the dual variables, which is found as the solution of a linear programming problem. We present a convergence proof, and demonstrate the successful solution tracking of the algorithm numerically on a couple of illustrative examples. Keywords: Parametric optimization, Predictorcorrector pathfollowing, Dualdegeneracy, Optimal solution sensitivity Category 1: Nonlinear Optimization Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Technical Report, Norwegian University of Science and Technology, March 2016 Download: [PDF] Entry Submitted: 03/30/2016 Modify/Update this entry  
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