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QPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints
"... . We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, firstlevel constraints are linear, and secondlevel (equilibrium) co ..."
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. We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, firstlevel constraints are linear, and secondlevel (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, illconditioning, convexity of the objective, monotonicity and symmetry of the secondlevel problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.maths.mu.OZ.AU/~danny/qpecgendoc.h...
An Approximation Algorithm for Stackelberg Network Pricing
 Networks
, 2005
"... Département d’informatique et de recherche opérationnelle, Université de Montréal, ..."
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Département d’informatique et de recherche opérationnelle, Université de Montréal,
BILEVEL PROGRAMMING: A COMBINATORIAL PERSPECTIVE
"... Bilevel programming is a branch of optimization where a subset of variables is constrained to lie in the optimal set of an auxiliary mathematical program. This chapter presents an overview of two specific classes of bilevel programs, and in particular their relationship to wellknown combinatorial p ..."
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Cited by 4 (1 self)
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Bilevel programming is a branch of optimization where a subset of variables is constrained to lie in the optimal set of an auxiliary mathematical program. This chapter presents an overview of two specific classes of bilevel programs, and in particular their relationship to wellknown combinatorial problems.
Geometry And Local Optimality Conditions For Bilevel Programs With Quadratic Strictly Convex Lower Levels
 In: D. Du, & M. Pardalos (Eds.), Minimax
, 1995
"... This paper describes necessary and sufficient optimality conditions for bilevel programming problems with quadratic strictly convex lower levels. By examining the local geometry of these problems we establish that the set of feasible directions at a given point is composed of a finite union of conve ..."
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Cited by 2 (0 self)
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This paper describes necessary and sufficient optimality conditions for bilevel programming problems with quadratic strictly convex lower levels. By examining the local geometry of these problems we establish that the set of feasible directions at a given point is composed of a finite union of convex cones. Based on this result, we show that the optimality conditions are simple generalizations of the first and second order optimality conditions for mathematical (one level) programming problems. 1 INTRODUCTION A bilevel program is defined as the problem of minimizing a function f (the upper level function) in two different vectors of variables x and y subject to (upper level) constraints, where the vector y is an optimal solution of another constrained optimization problem (the lower level problem) parameterized by the vector x. References [2] and [17] survey the extensive research that has been done in bilevel programming. 2 Chapter 1 It is interesting to note that any minimax probl...
Solving Method for a Class of Bilevel Linear Programming based on Genetic Algorithms ∗
"... The paper studies and designs an genetic algorithm (GA) of the bilevel linear programming problem (BLPP) by constructing the fitness function of the upperlevel programming problem based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints ..."
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The paper studies and designs an genetic algorithm (GA) of the bilevel linear programming problem (BLPP) by constructing the fitness function of the upperlevel programming problem based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into an initial population satisfying the constraints in order to improve the ability of the GA to deal with the constraints. Finally, the numerical results of some examples indicate the feasibility and effectiveness of the proposed method. Key words: bilevel linear programming, genetic algorithm, fitness function
A Hybrid TabuAscent Algorithm fo the Linear Bilevel Programming Problem
, 1996
"... . The linear Bilevel Programming Problem (BLP) is an instance of a linear hierarchical decision process where the lower level constraint set is dependent on decisions taken at the upper level. In this paper we propose to solve this NPhard problem using an adaptive search method related to the Tabu ..."
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. The linear Bilevel Programming Problem (BLP) is an instance of a linear hierarchical decision process where the lower level constraint set is dependent on decisions taken at the upper level. In this paper we propose to solve this NPhard problem using an adaptive search method related to the Tabu Search metaheuristic. Numerical results on large scale linear BLPs are presented. Keywords: Bilevel programming, adaptive search methods, combinatorial optimization, Tabu Search 1. Introduction In this paper we address the numerical solution of the linear bilevel problem (BLP) that consists in finding vectors x and y maximizing the linear form c 1 x+d 1 y, under the constraint that y be optimal for the lower level program 1 : max z d 2 z subject to Ax +Bz b z 0; where A is an m \Theta n x matrix and B an m \Theta n y matrix. The BLP is sometimes recorded in the following format: max x c 1 x + d 1 y max y d 2 y subject to Ax +By b (1) x; y 0: The feasible region P = f(x; y)j...
Fuzzy Goal Programming Approach to Quadratic BiLevel MultiObjective Programming Problem
"... This paper deals with fuzzy goal programming approach to quadratic bilevel multiobjective programming problem involving a single decision maker with multiple objectives at the upper level and a single decision maker with multiple objectives at the lower level. The objective functions of each level ..."
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This paper deals with fuzzy goal programming approach to quadratic bilevel multiobjective programming problem involving a single decision maker with multiple objectives at the upper level and a single decision maker with multiple objectives at the lower level. The objective functions of each level decision maker are quadratic in nature and the system constraints are linear functions. In the model formulation of the problem, we first determine the individual best solution of the quadratic objective functions subject to the system constraints and construct the quadratic membership functions of the objective functions of both levels. The quadratic membership functions are then transformed into equivalent linear membership functions by first order Taylor series at the individual best solution point. A possible relaxation of each level decision is considered by providing preference bounds on the decision variables for avoiding decision deadlock. Fuzzy goal programming approach is then used to achieve maximum degree of each of the membership goals by minimizing negative deviational variables. To demonstrate the efficiency of the proposed approach, an illustrative numerical example is provided.
Adversarial Label Flips Attack on Support Vector Machines
"... Abstract. To develop a robust classification algorithm in the adversarial setting, it is important to understand the adversary’s strategy. We address the problem of label flips attack where an adversary contaminates the training set through flipping labels. By analyzing the objective of the adversar ..."
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Abstract. To develop a robust classification algorithm in the adversarial setting, it is important to understand the adversary’s strategy. We address the problem of label flips attack where an adversary contaminates the training set through flipping labels. By analyzing the objective of the adversary, we formulate an optimization framework for finding the label flips that maximize the classification error. An algorithm for attacking support vector machines is derived. Experiments demonstrate that the accuracy of classifiers is significantly degraded under the attack. 1
Genetic Algorithm for Solving Convex Quadratic Bilevel Programming Problem ∗
"... Abstract: This paper presents a genetic algorithm method for solving convex quadratic bilevel programming problem. Bilevel programming problems arise when one optimization problem, the upper problem, is constrained by another optimization, the lower problem. In this paper, the bilevel convex quadrat ..."
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Abstract: This paper presents a genetic algorithm method for solving convex quadratic bilevel programming problem. Bilevel programming problems arise when one optimization problem, the upper problem, is constrained by another optimization, the lower problem. In this paper, the bilevel convex quadratic problem is transformed into a single level problem by applying KuhnTucker conditions, and then an efficient method based on genetic algorithm has been proposed for solving the transformed problem. By some rule, we simplify the transformed problem, so we can search the optimum solution in the feasible region, and reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is effective in practice. Key words: quadratic bilevel programming problem, genetic algorithm, optimal solution. AMS (MOS) subject classifications: 90C30 1
Chance Constrained Quadratic Bilevel Programming Problem
"... ABSTRACT: This paper deals with fuzzy goal programming approach to solve chance constrained quadratic bilevel programming problem. Chance constraints are converted into equivalent deterministic constraints by the prescribed distribution functions. In the model formulation, the quadratic membership ..."
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ABSTRACT: This paper deals with fuzzy goal programming approach to solve chance constrained quadratic bilevel programming problem. Chance constraints are converted into equivalent deterministic constraints by the prescribed distribution functions. In the model formulation, the quadratic membership functions are formulated by using the individual best solution of the quadratic objective functions subject to the equivalent deterministic constraints. Using first order Taylor’s series, the quadratic membership functions are approximated to linear membership functions expanding about the individual best solution points. For avoiding decision deadlock, each level decision maker provides a relaxation of bounds on the decision variables controlled by him. We use two fuzzy goal programming models to reach the highest degree of membership goals by minimizing negative deviational variables. Euclidean distance function is used to identify the most compromise optimal solution. To demonstrate the proposed approach, two numerical examples are solved.