Optimality conditions and strong duality in abstract and continuous-time linear programming

Meidan, Reuven; Perold, André F.

doi:10.1007/bf00934631

Cited by 15 publications

(4 citation statements)

References 8 publications

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“…Levinson [6] generalized the results of Tyndall by considering time-dependent matrices in which the functions appearing in the objective and constraints were assumed to be continuous on the time interval [0, T ]. Meidan and Perold [7], Papageorgiou [8] and Schechter [16] have also obtained some interesting results for the continuous-time linear programming problem. Anderson et al [1,2,3], Fleischer and Sethuraman [5] and Pullan [9,10,11,12,13] investigated a subclass of continuoustime linear programming problems, which is called separated continuous-time linear programming problem and can be used to model the job-shop scheduling problems.…”

Section: Introductionmentioning

confidence: 93%

Strong Duality Theorem for Continuous-Time Linear Programming Problems

2014

Preprint

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This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the case of piecewise continuous functions in which the discontinuities are the left-continuities. In this paper, we propose the completely different type of discretized primal and dual problems that can be used to prove the strong duality theorem for the general situation of discontinuities.

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Section: Introductionmentioning

confidence: 93%

Strong Duality Theorem for Continuous-Time Linear Programming Problems

2014

Preprint

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“…Meidan and Perold [18], Papageorgiou [21] and Schechter [32] have also obtained some interesting results of continuous-time linear programming problem. Anderson et al [1][2][3] , Fleischer and Sethuraman [9] and Pullan [23][24][25][26][27] investigated a subclass of continuous-time linear programming problem, which is called the separated continuous-time linear programming problem and can be used to model the job-shop scheduling problems.…”

Section: Introductionmentioning

confidence: 95%

Using the parametric approach to solve the continuous-time linear fractional max–min problems

Wen

2011

J Glob Optim

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A numerical algorithm based on parametric approach is proposed in this paper to solve a class of continuous-time linear fractional max-min programming problems. We shall transform this original problem into a continuous-time non-fractional programming problem, which unfortunately happens to be a continuous-time nonlinear programming problem. In order to tackle this nonlinear problem, we propose the auxiliary problem that will be formulated as a parametric continuous-time linear programming problem. We also introduce a dual problem of this parametric continuous-time linear programming problem in which the weak duality theorem also holds true. We introduce the discrete approximation method to solve the primal and dual pair of parametric continuous-time linear programming problems by using the recurrence method. Finally, we provide two numerical examples to demonstrate the usefulness of this algorithm.

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“…Owing to its special structure, many researchers such as Anderson et al [6][7][8], Fleischer and Sethuraman [9], and Pullan [10][11][12][13][14] have paid much attention to investigating its optimal solutions without providing the numerical technique. On the other hand, many interesting theoretical results have also been established by Meidan and Perold [15], Papageorgiou [16], and Schechter [17]. From the computational viewpoint, Weiss [18] designed a simplex-like algorithm that can be used to solve the separated continuous-time linear programming problem.…”

Section: Introductionmentioning

confidence: 99%

Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices

2021

Mathematics

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The uncertainty for the continuous-time linear programming problem with time-dependent matrices is considered in this paper. In this case, the robust counterpart of the continuous-time linear programming problem is introduced. In order to solve the robust counterpart, it will be transformed into the conventional form of the continuous-time linear programming problem with time-dependent matrices. The discretization problem is formulated for the sake of numerically calculating the ϵ-optimal solutions, and a computational procedure is also designed to achieve this purpose.

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Optimality conditions and strong duality in abstract and continuous-time linear programming

Cited by 15 publications

References 8 publications

Strong Duality Theorem for Continuous-Time Linear Programming Problems

Strong Duality Theorem for Continuous-Time Linear Programming Problems

Using the parametric approach to solve the continuous-time linear fractional max–min problems

Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices

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