Results 1  10
of
894
New necessary optimality conditions for bilevel programs by combining MPEC and the value function approach
 SIAM J. Optim
"... Abstract. The bilevel program is a sequence of two optimization problems where the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. The classical approach to solving such a problem is to replace the lower level problem by its Karus ..."
Abstract

Cited by 12 (7 self)
 Add to MetaCart
to define an equivalent single level problem. But the resulting problem requires a strong assumption, such as the partial calmness condition, for the KKT condition to hold. In this paper we combine the classical and the value function approaches to derive new necessary optimality conditions under rather
An overview of bilevel optimization
, 2007
"... This paper is devoted to bilevel optimization, a branch of mathematical programming of both practical and theoretical interest. Starting with a simple example, we proceed towards a general formulation. We then present fields of application, focus on solution approaches, and make the connection wit ..."
Abstract

Cited by 65 (3 self)
 Add to MetaCart
This paper is devoted to bilevel optimization, a branch of mathematical programming of both practical and theoretical interest. Starting with a simple example, we proceed towards a general formulation. We then present fields of application, focus on solution approaches, and make the connection
Modeling and Solution Environments for MPEC: GAMS
 Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods
, 1998
"... We describe several new tools for modeling MPEC problems that are built around the introduction of an MPEC model type into the GAMS language. We develop subroutines that allow such models to be communicated directly to MPEC solvers. This library of interface routines, written in the C language, prov ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
, and computational results are given that were obtained using all the tools described. Keywords Complementarity, Algorithm, MPEC, Modeling 1 Introduction The Mathematical Program with Equilibrium Constraints (MPEC) arises when one seeks to optimize an objective function subject to equilibrium contraints
Nonlinear Programming. 1. MPEC: APPLICATIONS AND CURRENT APPROACHES
"... Abstract: We discuss recent advances in mathematical programs with equilibrium constraints (MPECs). We describe the challenges posed by these problems and the current algorithmic solutions. We emphasize in particular the use of the elastic mode approach. We also present initial investigations in app ..."
Abstract
 Add to MetaCart
Abstract: We discuss recent advances in mathematical programs with equilibrium constraints (MPECs). We describe the challenges posed by these problems and the current algorithmic solutions. We emphasize in particular the use of the elastic mode approach. We also present initial investigations
Bilevel Optimization and Machine Learning
"... Abstract. We examine the interplay of optimization and machine learning. Great progress has been made in machine learning by cleverly reducing machine learning problems to convex optimization problems with one or more hyperparameters. The availability of powerful convexprogramming theory and algori ..."
Abstract
 Add to MetaCart
and algorithms has enabled a flood of new research in machine learning models and methods. But many of the steps necessary for successful machine learning models fall outside of the convex machine learning paradigm. Thus we now propose framing machine learning problems as Stackelberg games. The resulting bilevel
Strategic Gaming Analysis for Electric Power Systems: An MPEC Approach
 IEEE Transactions on Power Systems
, 2000
"... Transmission constraints and market concentration may prevent power markets from being fully competitive, allowing rms to exercise market power and raise prices above marginal cost. We present a strategic gaming model for analyzing such markets; it represents an oligopolistic market economy consisti ..."
Abstract

Cited by 87 (0 self)
 Add to MetaCart
consisting of several dominant rms in an electric power network. Each generating rm submits bids to an ISO, choosing its bids to maximize prots subject to anticipated reactions by rival rms. The singlerm model is formulated as a Mathematical Program with Equilibrium Constraints (MPEC) with a parameter
Some properties of regularization and penalization schemes for MPECs
 Optimization Methods and Software
, 2004
"... Abstract. Some properties of regularized and penalized nonlinear programming formulations of mathematical programs with equilibrium constraints (MPECs) are described. The focus is on the properties of these formulations near a local solution of the MPEC at which strong stationarity and a secondorde ..."
Abstract

Cited by 32 (2 self)
 Add to MetaCart
Abstract. Some properties of regularized and penalized nonlinear programming formulations of mathematical programs with equilibrium constraints (MPECs) are described. The focus is on the properties of these formulations near a local solution of the MPEC at which strong stationarity and a second
Model selection via bilevel programming
 Proceedings of the IEEE International Joint Conference on Neural Networks
, 2006
"... Support vector machines and related classification models require the solution of convex optimization problems that have one or more regularization hyperparameters. Typically, the hyperparameters are selected to minimize cross validated estimates of the outofsample classification error of the mo ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
of the model. This crossvalidation optimization problem can be formulated as a bilevel program in which the outerlevel objective minimizes the average number of misclassified points across the crossvalidation folds, subject to innerlevel constraints such that the classification functions for each fold
Results 1  10
of
894