Robust Solutions for Uncertain Continuous-Time Linear Programming Problems with Time-Dependent Matrices
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...
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| Veröffentlicht in: | Mathematics (Basel) Jg. 9; H. 8; S. 885 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Wu, Hsien-Chung |
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| Cites_doi | 10.1016/0022-247X(69)90106-1 10.1016/0022-247X(66)90187-9 10.1007/s10107-005-0678-0 10.1080/01630563.2016.1193517 10.1007/s10107-006-0710-z 10.1007/s10957-007-9301-2 10.3390/math7050435 10.1016/0022-247X(74)90124-3 10.1137/S0363012993257507 10.1007/s10898-011-9751-9 10.1137/S0363012992227216 10.1016/0022-247X(77)90072-5 10.1287/moor.23.4.769 10.1007/s10107-005-0679-z 10.1137/S0363012993247858 10.1016/0022-247X(82)90163-9 10.1006/jmaa.1997.5377 10.1137/0113043 10.1007/BF00934631 10.1016/0022-247X(80)90149-3 10.1016/0022-247X(78)90143-9 10.3934/math.2020358 10.1016/0022-247X(74)90280-7 10.1137/S0895479896298130 10.1137/0331073 10.1137/S1052623494278827 10.1016/0022-247X(72)90262-4 10.1287/opre.1030.0065 10.1007/s10107-002-0307-0 10.1137/S1052623496305717 10.1007/BF01303432 10.1016/S0167-6377(99)00016-4 10.1016/0022-247X(80)90278-4 10.1016/0022-247X(68)90184-4 10.1137/060650003 10.1006/jmaa.1998.6024 10.1007/s10957-007-9302-1 10.1007/s10107-005-0677-1 10.1287/opre.1070.0441 10.1080/01630563.2011.629312 10.1007/s10957-006-9082-z 10.1137/0321046 10.1007/s10107-008-0217-x 10.1287/moor.1050.0166 10.1007/s10898-010-9542-8 10.1137/0115112 10.1016/0022-247X(80)90230-9 10.1016/0022-247X(69)90143-7 |
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| References | Schechter (ref_17) 1972; 37 Nemirovski (ref_41) 1998; 23 Bertsimas (ref_48) 2004; 52 Bertsimas (ref_47) 2006; 108 Wu (ref_19) 2016; 37 Wen (ref_38) 2012; 54 Reil (ref_27) 1980; 74 Brandao (ref_29) 1998; 227 Anderson (ref_7) 1994; 32 Pullan (ref_10) 1993; 31 Boyd (ref_46) 2006; 107 ref_54 Singh (ref_28) 1978; 62 ref_53 Zhang (ref_52) 2007; 132 Dantzig (ref_40) 1955; 1 Iyengar (ref_51) 2006; 107 Wen (ref_39) 2012; 33 Zalmai (ref_35) 1990; 153 Oustry (ref_44) 1998; 9 Meidan (ref_15) 1983; 40 Reiland (ref_26) 1980; 77 Pullan (ref_12) 1996; 34 Pullan (ref_13) 2000; 10 Papageorgiou (ref_16) 1982; 87 Zalmai (ref_34) 1987; 31 Weiss (ref_18) 2008; 115 Pullan (ref_14) 2002; 93 Singh (ref_30) 1977; 59 Zalmai (ref_33) 1986; 30 Hanson (ref_24) 1968; 22 Tyndall (ref_3) 1967; 15 Farr (ref_21) 1974; 45 Reiland (ref_25) 1980; 77 Pullan (ref_11) 1995; 33 Grinold (ref_23) 1969; 28 Chen (ref_50) 2007; 55 Levinson (ref_4) 1966; 16 Zalmai (ref_36) 1997; 210 Anderson (ref_6) 1983; 21 Bertsimas (ref_49) 2006; 107 Farr (ref_20) 1974; 46 Wu (ref_5) 2020; 5 Anderson (ref_8) 1996; 43 Nobakhtian (ref_31) 2008; 136 Wen (ref_37) 2011; 49 Averbakh (ref_45) 2008; 18 ref_1 Grinold (ref_22) 1969; 27 Tyndall (ref_2) 1965; 15 Nemirovski (ref_42) 1999; 25 Nobakhtian (ref_32) 2008; 136 Lebret (ref_43) 1997; 18 Fleischer (ref_9) 2005; 30 |
| References_xml | – volume: 28 start-page: 32 year: 1969 ident: ref_23 article-title: Continuous Programming Part One: Linear Objectives publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(69)90106-1 – volume: 16 start-page: 73 year: 1966 ident: ref_4 article-title: A Class of Continuous Linear Programming Problems publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(66)90187-9 – volume: 107 start-page: 37 year: 2006 ident: ref_51 article-title: Ambiguous Chance Constrained Problems and Robust Optimization publication-title: Math. Program. doi: 10.1007/s10107-005-0678-0 – volume: 37 start-page: 1168 year: 2016 ident: ref_19 article-title: Solving the Continuous-Time Linear Programming Problems Based on the Piecewise Continuous Functions publication-title: Numer. Funct. Anal. Optim. doi: 10.1080/01630563.2016.1193517 – volume: 1 start-page: 197 year: 1955 ident: ref_40 article-title: Linear Programming under Uncertainty publication-title: Manag. Scienve – volume: 108 start-page: 251 year: 2006 ident: ref_47 article-title: Persistence in Discrete Optimization under Data Uncertainty publication-title: Math. Program. doi: 10.1007/s10107-006-0710-z – volume: 136 start-page: 77 year: 2008 ident: ref_32 article-title: Duality for Nonsmooth Continuous-Time Problems of Vector Optimization publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-007-9301-2 – ident: ref_53 doi: 10.3390/math7050435 – volume: 45 start-page: 96 year: 1974 ident: ref_21 article-title: Continuous Time Programming with Nonlinear Constraints publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(74)90124-3 – volume: 34 start-page: 931 year: 1996 ident: ref_12 article-title: A Duality Theory for Separated Continuous Linear Programs publication-title: Siam J. Control. Optim. doi: 10.1137/S0363012993257507 – ident: ref_1 – volume: 30 start-page: 43 year: 1986 ident: ref_33 article-title: Duality for a Class of Continuous-Time Homogeneous Fractional Programming Problems publication-title: Z. Oper. Res. Ser. A B – volume: 54 start-page: 129 year: 2012 ident: ref_38 article-title: Using the Parametric Approach to Solve the Continuous-Time Linear Fractional Max-Min Problems publication-title: J. Glob. Optim. doi: 10.1007/s10898-011-9751-9 – volume: 31 start-page: 209 year: 1987 ident: ref_34 article-title: Duality for a Class of Continuous-Time Fractional Programming Problems publication-title: Util. Math. – volume: 32 start-page: 1289 year: 1994 ident: ref_7 article-title: On the Solutions of a Class of Continuous Linear Programs publication-title: Siam J. Control. Optim. doi: 10.1137/S0363012992227216 – volume: 59 start-page: 442 year: 1977 ident: ref_30 article-title: Saddle-Point Optimality Criteria of Continuous Time Programming without Differentiability publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(77)90072-5 – volume: 23 start-page: 769 year: 1998 ident: ref_41 article-title: Robust Convex Optimization publication-title: Math. Oper. Res. doi: 10.1287/moor.23.4.769 – volume: 107 start-page: 63 year: 2006 ident: ref_46 article-title: Extending Scope of Robust Optimization: Comprehensive Robust Counterpart of Uncertain Problems publication-title: Math. Program. doi: 10.1007/s10107-005-0679-z – volume: 33 start-page: 1952 year: 1995 ident: ref_11 article-title: Forms of Optimal Solutions for Separated Continuous Linear Programs publication-title: Siam J. Control. Optim. doi: 10.1137/S0363012993247858 – volume: 87 start-page: 228 year: 1982 ident: ref_16 article-title: A Class of Infinite Dimensional Linear Programming Problems publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(82)90163-9 – volume: 210 start-page: 114 year: 1997 ident: ref_36 article-title: Optimality Conditions and Duality models for a Class of Nonsmooth Constrained Fractional Optimal Control Problems publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1997.5377 – volume: 15 start-page: 644 year: 1965 ident: ref_2 article-title: A Duality Theorem for a Class of Continuous Linear Programming Problems publication-title: SIAM J. Appl. Math. doi: 10.1137/0113043 – volume: 40 start-page: 61 year: 1983 ident: ref_15 article-title: Optimality Conditions and Strong Duality in Abstract and Continuous-Time Linear Programming publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00934631 – volume: 74 start-page: 578 year: 1980 ident: ref_27 article-title: Generalized Kuhn-Tucker Conditions and Duality for Continuous Nonlinear Programming Problems publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(80)90149-3 – volume: 62 start-page: 506 year: 1978 ident: ref_28 article-title: A Sufficient Optimality Criterion in Continuous Time Programming for Generalized Convex Functions publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(78)90143-9 – volume: 5 start-page: 5572 year: 2020 ident: ref_5 article-title: Numerical Method for Solving the Continuous-Time Linear Programming Problems with Time-Dependent Matrices and Piecewise Continuous Functions publication-title: Aims Math. doi: 10.3934/math.2020358 – volume: 46 start-page: 41 year: 1974 ident: ref_20 article-title: Continuous Time Programming with Nonlinear Time-Delayed publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(74)90280-7 – volume: 18 start-page: 1035 year: 1997 ident: ref_43 article-title: Robust Solutions to Least-Squares Problems with Uncertain Data publication-title: Siam J. Matrix Anal. Appl. doi: 10.1137/S0895479896298130 – volume: 31 start-page: 1558 year: 1993 ident: ref_10 article-title: An Algorithm for a Class of Continuous Linear Programs publication-title: Siam J. Control. Optim. doi: 10.1137/0331073 – volume: 10 start-page: 722 year: 2000 ident: ref_13 article-title: Convergence of a General Class of Algorithms for Separated Continuous Linear Programs publication-title: Siam J. Optim. doi: 10.1137/S1052623494278827 – volume: 37 start-page: 130 year: 1972 ident: ref_17 article-title: Duality in Continuous Linear Programming publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(72)90262-4 – volume: 52 start-page: 35 year: 2004 ident: ref_48 article-title: The Price of Robustness publication-title: Oper. Res. doi: 10.1287/opre.1030.0065 – volume: 93 start-page: 415 year: 2002 ident: ref_14 article-title: An Extended Algorithm for Separated Continuous Linear Programs publication-title: Math. Program. doi: 10.1007/s10107-002-0307-0 – volume: 153 start-page: 365 year: 1990 ident: ref_35 article-title: Optimality Conditions and Duality for a Class of Continuous-Time Generalized Fractional Programming Problems publication-title: J. Math. Anal. Appl. – volume: 9 start-page: 33 year: 1998 ident: ref_44 article-title: Robust Solutions to Uncertain Semidefinite Programs publication-title: Siam J. Optim. doi: 10.1137/S1052623496305717 – volume: 43 start-page: 9 year: 1996 ident: ref_8 article-title: Purification for Separated Continuous Linear Programs publication-title: Math. Methods Oper. Res. doi: 10.1007/BF01303432 – volume: 25 start-page: 1 year: 1999 ident: ref_42 article-title: Robust Solutions of Uncertain Linear Programs publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(99)00016-4 – volume: 77 start-page: 297 year: 1980 ident: ref_25 article-title: Optimality Conditions and Duality in Continuous Programming I: Convex Programs and a Theorem of the Alternative publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(80)90278-4 – volume: 22 start-page: 427 year: 1968 ident: ref_24 article-title: A Class of Continuous Convex Programming Problems publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(68)90184-4 – volume: 18 start-page: 1436 year: 2008 ident: ref_45 article-title: Explicit Reformulations for Robust Optimization Problems with General Uncertainty Sets publication-title: Siam J. Optim. doi: 10.1137/060650003 – volume: 227 start-page: 305 year: 1998 ident: ref_29 article-title: Nonsmooth Continuous-Time Optimization Problems: Sufficient Conditions publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1998.6024 – ident: ref_54 – volume: 136 start-page: 69 year: 2008 ident: ref_31 article-title: Optimality Criteria for Nonsmooth Continuous-Time Problems of Multiobjective Optimization publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-007-9302-1 – volume: 107 start-page: 5 year: 2006 ident: ref_49 article-title: Tractable Approximations to Robust Conic Optimization Problems publication-title: Math. Program. doi: 10.1007/s10107-005-0677-1 – volume: 55 start-page: 1058 year: 2007 ident: ref_50 article-title: A Robust Optimization Perspective on Stochastic Programming publication-title: Oper. Res. doi: 10.1287/opre.1070.0441 – volume: 33 start-page: 80 year: 2012 ident: ref_39 article-title: The Approximate Solutions and Duality Theorems for the Continuous-Time Linear Fractional Programming Problems publication-title: Numer. Funct. Anal. Optim. doi: 10.1080/01630563.2011.629312 – volume: 132 start-page: 111 year: 2007 ident: ref_52 article-title: General Robust Optimization Formulation for Nonlinear Programming publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-006-9082-z – volume: 21 start-page: 758 year: 1983 ident: ref_6 article-title: Some Properties of a Class of Continuous Linear Programs publication-title: Siam Control. Optim. doi: 10.1137/0321046 – volume: 115 start-page: 151 year: 2008 ident: ref_18 article-title: A Simplex Based Algorithm to Solve Separated Continuous Linear Programs publication-title: Math. Program. doi: 10.1007/s10107-008-0217-x – volume: 30 start-page: 916 year: 2005 ident: ref_9 article-title: Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions publication-title: Math. Oper. Res. doi: 10.1287/moor.1050.0166 – volume: 49 start-page: 237 year: 2011 ident: ref_37 article-title: Using the Dinkelbach-Type Algorithm to Solve the Continuous-Time Linear Fractional Programming Problems publication-title: J. Glob. Optim. doi: 10.1007/s10898-010-9542-8 – volume: 15 start-page: 1294 year: 1967 ident: ref_3 article-title: An Extended Duality Theorem for Continuous Linear Programming Problems publication-title: SIAM J. Appl. Math. doi: 10.1137/0115112 – volume: 77 start-page: 329 year: 1980 ident: ref_26 article-title: Optimality Conditions and Duality in Continuous Programming II: The Linear Problem Revisited publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(80)90230-9 – volume: 27 start-page: 639 year: 1969 ident: ref_22 article-title: Continuous Programming Part Two: Nonlinear Objectives publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(69)90143-7 |
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