Corrigendum: On the Constant Positive Linear Dependence Condition and Its Application to SQP Methods

We correct an assertion in the quoted paper [Qi and Wei, SIAM J. Optim., 10 (2000), pp. 963--981].

[1]  André L. Tits,et al.  On combining feasibility, descent and superlinear convergence in inequality constrained optimization , 1993, Math. Program..

[2]  L. Qi,et al.  Newton's method for quadratic stochastic programs with recourse , 1995 .

[3]  Xiaojun Chen,et al.  Convergence of the BFGS Method for LC 1 Convex Constrained Optimization , 1996 .

[4]  J. Stoer,et al.  Convexity and Optimization in Finite Dimensions I , 1970 .

[5]  S. M. Robinson First Order Conditions for General Nonlinear Optimization , 1976 .

[6]  M. J. D. Powell,et al.  THE CONVERGENCE OF VARIABLE METRIC METHODS FOR NONLINEARLY CONSTRAINED OPTIMIZATION CALCULATIONS , 1978 .

[7]  Jong-Shi Pang,et al.  Piecewise Smoothness, Local Invertibility, and Parametric Analysis of Normal Maps , 1996, Math. Oper. Res..

[8]  Zengxin Wei,et al.  On the Constant Positive Linear Dependence Condition and Its Application to SQP Methods , 1999, SIAM J. Optim..

[9]  Shih-Ping Han,et al.  Superlinearly convergent variable metric algorithms for general nonlinear programming problems , 1976, Math. Program..

[10]  Olvi L. Mangasarian,et al.  Superlinearly convergent quasi-newton algorithms for nonlinearly constrained optimization problems , 1976, Math. Program..

[11]  S. M. Robinson Generalized equations and their solutions, part II: Applications to nonlinear programming , 1982 .

[12]  Stephen M. Robinson,et al.  Strongly Regular Generalized Equations , 1980, Math. Oper. Res..

[13]  Houyuan Jiang,et al.  Globally and superlinearly convergent trust-region algorithm for convex SC1-minimization problems and its application to stochastic programs , 1996 .

[14]  Liqun Qi,et al.  Superlinearly convergent approximate Newton methods for LC1 optimization problems , 1994, Math. Program..

[15]  Houyuan Jiang,et al.  Semismooth Karush-Kuhn-Tucker Equations and Convergence Analysis of Newton and Quasi-Newton Methods for Solving these Equations , 1997, Math. Oper. Res..

[16]  R. Janin Directional derivative of the marginal function in nonlinear programming , 1984 .

[17]  J. F. Bonnans Local study of Newton type algorithms for constrained problems , 1988 .

[18]  Stephen M. Robinson,et al.  Lower Semicontinuity of Multivalued Linearization Mappings , 1973 .

[19]  Francisco Facchinei,et al.  Minimization of SC1 functions and the Maratos effect , 1995, Oper. Res. Lett..

[20]  J. Pang,et al.  Stability analysis of variational inequalities and nonlinear complementarity problems, via the mixed linear complementarity problem and degree theory , 1994 .

[21]  Datong Sun,et al.  A computable generalized Hessian of the D - gap function and Newton - type methods for variational i , 1997 .

[22]  Liqun Qi,et al.  An SQP algorithm for extended linear-quadratic problems in stochastic programming , 1995, Ann. Oper. Res..

[23]  Elijah Polak,et al.  Globally and Superlinearly Convergent Algorithm for Minimizing a Normal Merit Function , 1998 .

[24]  M. Kojima Strongly Stable Stationary Solutions in Nonlinear Programs. , 1980 .

[25]  Houyuan Jiang,et al.  Semismoothness and Superlinear Convergence in Nonsmooth Optimization and Nonsmooth Equations , 1996 .

[26]  Stephen J. Wright,et al.  Superlinear convergence of an interior-point method for monotone variational inequalities , 1996 .

[27]  Stephen J. Wright Superlinear Convergence of a Stabilized SQP Method to a Degenerate Solution , 1998, Comput. Optim. Appl..

[28]  Elijah Polak,et al.  Optimization: Algorithms and Consistent Approximations , 1997 .

[29]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[30]  E. Panier,et al.  A superlinearly convergent feasible method for the solution of inequality constrained optimization problems , 1987 .

[31]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

[32]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[33]  J. Pang,et al.  A globally convergent Newton method for convex SC1 minimization problems , 1995 .

[34]  Defeng Sun,et al.  Superlinear Convergence of Approximate Newton Methods for LC1 Optimization Problems without Strict Complementarity , 1995 .