A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints
نویسندگان
چکیده
In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, NP-hard Linear Complementarity Problems, and Hinge Fitting Problems are presented to highlight the efficacy of the procedure in determining a global minimum for different classes of MPECs.
منابع مشابه
On linear programs with linear complementarity constraints
The paper is a manifestation of the fundamental importance of the linear program with linear complementarity constraints (LPCC) in disjunctive and hierarchical programming as well as in some novel paradigms of mathematical programming. In addition to providing a unified framework for bilevel and inverse linear optimization, nonconvex piecewise linear programming, indefinite quadratic programs, ...
متن کاملA Class of Mathematical Programs with Equilibrium Constraints: A Smooth Algorithm and Applications to Contact Problems
We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod or a plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicity defined by the solution of a mixed linear complementarity p...
متن کاملGlobal Solution to Parametric Complementarity Constrained Programs and Applications in Optimal Parameter Selection By
This thesis contains five chapters. The notations, terminologies, definitions and numbering of equations, theorems and algorithms are independent in each chapter. Chapter 1 provides a fundamental introduction and contextual discussions to provide a unified theme for the subsequent chapters into a complete work. Chapters 2, 3 and 4 are arranged for ease of reading and understanding separately. F...
متن کاملA Complementarity Active-Set Algorithm for Mathematical Programming Problems with Equilibrium Constraints
In this paper, an algorithm for solving a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPEC) is introduced, which uses the active-set methodology while maintaining the complementarity restrictions throughout the procedure. Finite convergence of the algorithm to a stationary point of the MPEC is established under reasonable hypotheses. The algorithm can be ...
متن کاملSolving Linear Programs with Complementarity Constraints using Branch-and-Cut
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a modeling paradigm for a broad collection of problems, including bilevel programs, Stackelberg games, inverse quadratic programs, and problems involving equilibrium...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Global Optimization
دوره 36 شماره
صفحات -
تاریخ انتشار 2006