Equivalent primal and dual differentiable reformulations of the Euclidean multifacility location problem.: An article from: IIE Transactions
Book Details
ISBN / ASINB00098TRV6
ISBN-13978B00098TRV7
AvailabilityAvailable for download now
Sales Rank99,999,999
MarketplaceUnited States 🇺🇸
Description
This digital document is an article from IIE Transactions, published by Institute of Industrial Engineers, Inc. (IIE) on November 1, 1998. The length of the article is 8243 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.
From the author: In this paper, we consider two equivalent differentiable reformulations of the nondifferentiable Euclidean multifacility location problem (EMFLP). The first of these is derived via a Lagrangian dual approach based on the optimum of a linear function over a unit ball (circle). The resulting formulation turns out to be identical to the known dual problem proposed by Francis and Cabot [1]. Hence, besides providing an easy direct derivation of the dual problem, this approach lends insights into its connections with classical Lagrangian duality and related results. In particular, it characterizes a straightforward recovery of primal location decisions. The second equivalent differentiable formulation is constructed directly in the primal space. Although the individual constraints of the resulting problem are generally nonconvex, we show that their intersection represents a convex feasible region. We then establish the relationship between the Karush Kuhn-Tucker (KKT) conditions for this problem and the necessary and sufficient optimality conditions for EMFLP. This lends insights into the possible performance of standard differentiable nonlinear programming algorithms when applied to solve this reformulated problem. Some computational results on test problems from the literature, and other randomly generated problems, are also provided.
Citation Details
Title: Equivalent primal and dual differentiable reformulations of the Euclidean multifacility location problem.
Author: Hanif D. Sherali
Publication:IIE Transactions (Refereed)
Date: November 1, 1998
Publisher: Institute of Industrial Engineers, Inc. (IIE)
Volume: 30 Issue: 11 Page: 1065(1)
Distributed by Thomson Gale
From the author: In this paper, we consider two equivalent differentiable reformulations of the nondifferentiable Euclidean multifacility location problem (EMFLP). The first of these is derived via a Lagrangian dual approach based on the optimum of a linear function over a unit ball (circle). The resulting formulation turns out to be identical to the known dual problem proposed by Francis and Cabot [1]. Hence, besides providing an easy direct derivation of the dual problem, this approach lends insights into its connections with classical Lagrangian duality and related results. In particular, it characterizes a straightforward recovery of primal location decisions. The second equivalent differentiable formulation is constructed directly in the primal space. Although the individual constraints of the resulting problem are generally nonconvex, we show that their intersection represents a convex feasible region. We then establish the relationship between the Karush Kuhn-Tucker (KKT) conditions for this problem and the necessary and sufficient optimality conditions for EMFLP. This lends insights into the possible performance of standard differentiable nonlinear programming algorithms when applied to solve this reformulated problem. Some computational results on test problems from the literature, and other randomly generated problems, are also provided.
Citation Details
Title: Equivalent primal and dual differentiable reformulations of the Euclidean multifacility location problem.
Author: Hanif D. Sherali
Publication:IIE Transactions (Refereed)
Date: November 1, 1998
Publisher: Institute of Industrial Engineers, Inc. (IIE)
Volume: 30 Issue: 11 Page: 1065(1)
Distributed by Thomson Gale
