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In view of solving nonsmooth and nonconvex problems involving complexconstraints (like standard NLP problems), we study generalmaximization-minimization procedures produced by families of strongly convexsub-problems. Using techniques from semi-algebraic geometry and variationalanalysis -in particular Lojasiewicz inequality- we establish the convergence ofsequences generated by this type of schemes to critical points. The broadapplicability of this process is illustrated in the context of NLP. In thatcase critical points coincide with KKT points. When the data are semi-algebraicor real analytic our method applies (for instance) to the study of various SQPmethods: the moving balls method, Sl1QP, ESQP. Under standard qualificationconditions, this provides -to the best of our knowledge- the first generalconvergence results for general nonlinear programming problems. We emphasizethe fact that, unlike most works on this subject, no second-order assumptionand/or convexity assumptions whatsoever are made. Rate of convergence are shownto be of the same form as those commonly encountered with first order methods.

Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs