bilevelprogramming, one of the multilevel programming, is a class of optimization with hierarchical structure. This paper proposes a globally convergent algorithm for a class of bilevel nonlinear programming. In this...
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bilevelprogramming, one of the multilevel programming, is a class of optimization with hierarchical structure. This paper proposes a globally convergent algorithm for a class of bilevel nonlinear programming. In this algorithm, by use of the dual theory, the bilevel nonlinear programming is transformed into a traditional programming problem, which can be turned into a series of programming problem without constraints. So we can solve the infinite nonlinearprogramming in parallelism to obtain the globally convergent solution of the original bilevel nonlinear programming. And the example illustrates the feasibility and efficiency of the proposed algorithm. (C) 2006 Elsevier Inc. All rights reserved.
Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex optimization problems, that includes, among others, generalized polynomial programming, genera...
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Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex optimization problems, that includes, among others, generalized polynomial programming, generalized multiplicative and fractional programming, discrete programming, optimization over the efficient set, complementarity problems. In the present paper the monotonic approach is extended to the General bilevelprogramming GBP Problem. It is shown that (GBP) can be transformed into a monotonic optimization problem which can then be solved by "polyblock" approximation or, more efficiently, by a branch-reduce-and-bound method using monotonicity cuts. The method is particularly suitable for bilevel Convex programming and bilevel Linear programming.
Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex optimization problems, that includes, among others, generalized polynomial programming, genera...
详细信息
Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex optimization problems, that includes, among others, generalized polynomial programming, generalized multiplicative and fractional programming, discrete programming, optimization over the efficient set, complementarity problems. In the present paper the monotonic approach is extended to the General bilevelprogramming GBP Problem. It is shown that (GBP) can be transformed into a monotonic optimization problem which can then be solved by "polyblock" approximation or, more efficiently, by a branch-reduce-and-bound method using monotonicity cuts. The method is particularly suitable for bilevel Convex programming and bilevel Linear programming.
While significant progress has been made, analytic research on principal-agent problems that seek closed-form solutions faces limitations due to tractability issues that arise because of the mathematical complexity of...
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While significant progress has been made, analytic research on principal-agent problems that seek closed-form solutions faces limitations due to tractability issues that arise because of the mathematical complexity of the problem. The principal must maximize expected utility subject to the agent's participation and incentive compatibility constraints. Linearity of performance measures is often assumed and the Linear, Exponential, Normal (LEN) model is often used to deal with this complexity. These assumptions may be too restrictive for researchers to explore the variety of relationships between compensation contracts offered by the principal and the effort of the agent. In this paper we show how to numerically solve principal-agent problems with nonlinear contracts. In our procedure, we deal directly with the agent's incentive compatibility constraint. We illustrate our solution procedure with numerical examples and use optimization methods to make the problem tractable without using the simplifying assumptions of a LEN model. We also show that using linear contracts to approximate nonlinear contracts leads to solutions that are far from the optimal solutions obtained using nonlinear contracts. A principal-agent problem is a special instance of a bilevel nonlinear programming problem. We show how to solve principal-agent problems by solving bilevelprogramming problems using the ellipsoid algorithm. The approach we present can give researchers new insights into the relationships between nonlinear compensation schemes and employee effort. (C) 2013 Elsevier B.V. All rights reserved.
Many real problems can be modeled to the problems with a hierarchical structure, and bilevelprogramming is a useful tool to solve the hierarchical optimization problems. So the bilevelprogramming is widely applied, ...
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Many real problems can be modeled to the problems with a hierarchical structure, and bilevelprogramming is a useful tool to solve the hierarchical optimization problems. So the bilevelprogramming is widely applied, and numerous methods have been proposed to solve this programming. In this paper, we propose an approximate programming algorithm to solve bilevel nonlinear programming problem. Finally, the example illustrates the feasibility of the proposed algorithm. (C) 2010 Elsevier Ltd. All rights reserved.
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