On solving a D.C. programming problem by a sequence of linear programs

Horst, Reiner; Phong, Thai Quynh; Thoại, Nguyễn Văn; Vries, Jakob de

doi:10.1007/bf00119991

Cited by 61 publications

(29 citation statements)

References 34 publications

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“…In this case, both the default model and the alternative model fall in the category of Difference of Convex functions (DC) programming. In the literature, there exist good numerical methods to find local optima of DC models, see Horst et al 1991;Pham Dinh and Le Thi 2014. However, to guarantee global optimality such methods need to be incorporated into for example a Branch-andBound procedure.…”

Section: Alternative Convex Modelmentioning

confidence: 99%

Two-echelon supply chain coordination under information asymmetry with multiple types

Kerkkamp

Heuvel

Wagelmans

2018

Omega

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We analyse a principal-agent contracting model with asymmetric information between a supplier and a retailer. Both the supplier and the retailer have the classical non-linear economic ordering cost functions consisting of ordering and holding costs. We assume that the retailer has the market power to enforce any order quantity. Furthermore, the retailer has private holding costs. The supplier wants to minimise his expected costs by offering a menu of contracts with side payments as an incentive mechanism. We consider a general number of discrete singledimensional retailer types with type-dependent default options.A natural and common model formulation is non-convex, but we present an equivalent convex formulation. Hence, the contracting model can be solved efficiently for a general number of retailer types. We also derive structural properties of the optimal menu of contracts. In particular, we completely characterise the optimum for two retailer types and provide a minimal list of candidate contracts for three types. Finally, we prove a sufficient condition to guarantee unique contracts in the optimal solution for a general number of retailer types.

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Section: Alternative Convex Modelmentioning

confidence: 99%

Two-echelon supply chain coordination under information asymmetry with multiple types

Kerkkamp

Heuvel

Wagelmans

2018

Omega

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“…The considered decomposition enables the application of certain results from the DC programming theory. We adopt a prismatic branch and bound algorithm (prism algorithm) [11], which yields a global optimum. We show how all necessary ingredients (including gradients and polyhedral approximation) of the algorithm can be obtained by exploiting the special structure of the interference functions.…”

Section: Contributionsmentioning

confidence: 99%

“…The prism algorithm, however, is numerically efficient compared with e.g., the one utilizing conical or simplicial partitions. It combines prismatic partitions and polyhedral outer approximation procedure in such a way only linear programs have to be solved in each iteration [11].…”

Section: Contributionsmentioning

confidence: 99%

Globally Optimal Resource Allocation for Achieving Maximum Weighted Sum Rate

Eriksson

Shi

Vučić³

et al. 2010

2010 IEEE Global Telecommunications Conference GLOBECOM 2010

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We establish a general optimization framework for joint resource allocation and interference mitigation. By utilizing axiomatic interference functions, our problem formulation is very general and includes many problems as special cases. We consider the sum rate maximization problem, which is known to be NP hard. It is shown that due to the structural model of the interference function, the joint optimization of powers and adaptive receive strategies ends up with the optimization solely with respect to powers. This facilitates a reformulation of the problem under consideration as a problem of difference of convex functions (DC). Based on this DC representation, we employ a prismatic branch and bound algorithm to find a global optimum.Index Terms-Optimal resource management, DC programming, interference mitigation, MIMO systems, power control.

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“…Horst, Phong, Thoai and Vries [52] proposed an algorithm for solving the bounded case of this problem. This algorithm combines the branch and bound technique, and the outer approximation technique.…”

Section: General Constrained DC Optimization Problemsmentioning

confidence: 99%

Outer approximation algorithms for DC programs and beyond

Zhang

2010

4OR-Q J Oper Res

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On solving a D.C. programming problem by a sequence of linear programs

Cited by 61 publications

References 34 publications

Two-echelon supply chain coordination under information asymmetry with multiple types

Two-echelon supply chain coordination under information asymmetry with multiple types

Globally Optimal Resource Allocation for Achieving Maximum Weighted Sum Rate

Outer approximation algorithms for DC programs and beyond

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