Mathematical Programs with Complementarity Constraints in Banach Spaces

نویسنده

  • Gerd Wachsmuth
چکیده

We consider optimization problems in Banach spaces involving a complementarity constraint defined by a convex cone K. By transferring the local decomposition approach, we define strong stationarity conditions and provide a constraint qualification under which these conditions are necessary for optimality. To apply this technique, we provide a new uniqueness result for Lagrange multipliers in Banach spaces. Under the additional assumption that the cone K is polyhedral, we show that our strong stationarity conditions possess a reasonable strength. Finally, we generalize to the case that K is not a cone and apply the theory to two examples.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Mangasarian-Fromovitz and Zangwill Conditions For Non-Smooth Infinite Optimization problems in Banach Spaces

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are Lipschitz near the optimal solution. Necessary optimality conditions and constraint qualifications in terms of Michel-Penot subdifferential are given.

متن کامل

Linear operators of Banach spaces with range in Lipschitz algebras

In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.

متن کامل

Smoothing method for mathematical programs with symmetric cone complementarity constraints

In this paper, we consider the mathematical program with symmetric cone complementarity constraints (MPSCCC) in a general form. It includes the mathematical program with second-order-cone complementarity constraints (MPSOCCC) and the mathematical program with complementarity constraints (MPCC). We present a smoothing method which approximates the primal MPSCCC by means of the ChenMangasarian cl...

متن کامل

Vector mixed quasi complementarity problems in Banach spaces

In this paper, we introduce a new class of set-valued vector implicit quasi complementarity problemswith corresponding set-valued implicit quasi variational inequality problems. By means of the Fan–KKM theorem, we investigate the nonemptiness and compactness of solution sets of these problems. Our work generalizes and improves some results appeared recently in the literature. © 2011 Elsevier Lt...

متن کامل

A Class of Quadratic Programs with Linear Complementarity Constraints

We consider a class of quadratic programs with linear complementarity constraints (QPLCC) which belong to mathematical programs with equilibrium constraints (MPEC). We investigate various stationary conditions and present new and strong necessary and sufficient conditions for global and local optimality. Furthermore, we propose a Newton-like method to find an M-stationary point in finite steps ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Optimization Theory and Applications

دوره 166  شماره 

صفحات  -

تاریخ انتشار 2015