Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity

Francisco Facchinei (), Vyacheslav Kungurtsev (), Lorenzo Lampariello () and Gesualdo Scutari ()
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Francisco Facchinei: Department of Computer, Control, and Management Engineering Antonio Ruberti, Sapienza University of Rome, 00185 Rome, Italy
Vyacheslav Kungurtsev: Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague, 12135 Prague, Czech Republic
Lorenzo Lampariello: Department of Business Studies, Roma Tre University, 00145 Rome, Italy
Gesualdo Scutari: School of Industrial Engineering, Purdue University, West Lafayette, Indiana 47097

Mathematics of Operations Research, 2021, vol. 46, issue 2, 595-627

Abstract: We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. We make use of classical penalty functions in an unconventional way, in that penalty functions only enter in the theoretical analysis of convergence while the algorithm itself is penalty free. Based on this idea, we are able to establish several new results, including the first general analysis for diminishing stepsize methods in nonconvex, constrained optimization, showing convergence to generalized stationary points, and a complexity study for sequential quadratic programming–type algorithms.

Keywords: Primary: 90C30; 90C60; 65K05; Primary: Programming: nonlinear algorithms; secondary: analysis of algorithms: computational complexity; constrained optimization; nonconvex problem; diminishing stepsize; generalized stationary point; iteration complexity (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:2:p:595-627

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