Abstract
It is shown that a Lagrange multiplier rule that uses approximate Jacobians holds for mathematical programming problems involving Lipschitzian functions, finitely many equality constraints, and convex set constraints. It is sharper than the corresponding Lagrange multiplier rules for the convex-valued subdifferentials such as those of Clarke [Optimization and Nonsmooth Analysis, 2nd ed., SIAM, 1990] and Michel and Penot [Differential Integral Equations, 5 (1992), pp. 433--454]. The Lagrange multiplier result is obtained by means of a controllability criterion and the theory of fans developed by A. D. Ioffe [Math. Oper. Res., 9 (1984), pp. 159--189, Math. Programming, 58 (1993), pp. 137--145]. As an application, necessary optimality conditions are derived for a class of constrained minimax problems. An example is discussed to illustrate the nature of the multiplier rule.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
