Trust Region Approaches for Nonlinear Bilevel Programming
نویسندگان
چکیده
Bilevel programs form a class of hierarchical optimzation problems in which the constraint set is not explicit but is defined in terms of another optimization problem. Optimization problems in several real-life domains can be expressed as bilevel programs, making such problems ubiquitous. In this term paper, we analyze a trust region approach for solving a special case of this problem.
منابع مشابه
A trust region algorithm for nonlinear bilevel programming
We propose to solve generalized bilevel programs by a trust region approach where the “model” takes the form of a bilevel program involving a linear program at the upper level and a linear variational inequality at the lower level. By coupling the concepts of trust region and linesearch in a novel way, we obtain an implementable algorithm that converges to a strong stationary point of the origi...
متن کاملA Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience
We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all constraintdefining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Numerical experiments...
متن کاملALGORITHMS FOR BILEVEL OPTIMIZATIONNatalia
General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multicriteria optimization problems. Here for clarity in displaying our ideas, we restrict ourselves to general bilevel optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easi...
متن کاملA TRUST-REGION SEQUENTIAL QUADRATIC PROGRAMMING WITH NEW SIMPLE FILTER AS AN EFFICIENT AND ROBUST FIRST-ORDER RELIABILITY METHOD
The real-world applications addressing the nonlinear functions of multiple variables could be implicitly assessed through structural reliability analysis. This study establishes an efficient algorithm for resolving highly nonlinear structural reliability problems. To this end, first a numerical nonlinear optimization algorithm with a new simple filter is defined to locate and estimate the most ...
متن کاملSQP methods for large - scalenonlinear programmingby
We compare and contrast a number of recent sequential quadratic programming (SQP) methods that have been proposed for the solution of large-scale nonlinear programming problems. Both line-search and trust-region approaches are considered, as are the implications of interior-point and quadratic programming methods.
متن کامل