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Zeitschriftenartikel zum Thema „Programming functions“

Autor: Grafiati

Veröffentlicht am 28. Juni 2021

Zuletzt aktualisiert am 7. Februar 2022

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1

Neralić, Luka, and Sanjo Zlobec. "LFS functions in multi-objective programming." Applications of Mathematics 41, no. 5 (1996): 347–66. http://dx.doi.org/10.21136/am.1996.134331.

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2

Odersky, Martin. "Programming with variable functions." ACM SIGPLAN Notices 34, no. 1 (1999): 105–16. http://dx.doi.org/10.1145/291251.289433.

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3

Rhodes, Frank, and H. Paul Williams. "Discrete subadditive functions as Gomory functions." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 3 (1995): 559–74. http://dx.doi.org/10.1017/s0305004100073370.

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Our aim, in this paper, is to study a class of functions which occurs in pure integer programming, and to investigate conditions under which discrete subadditive functions belong to that class. The inspiration for the paper was the problem of classifying discrete metrics used in pattern recognition, while the methods of proof of the main theorem are those of pure integer programming.

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4

Baykasoğlu, Adil, and Sultan Maral. "Fuzzy functions via genetic programming." Journal of Intelligent & Fuzzy Systems 27, no. 5 (2014): 2355–64. http://dx.doi.org/10.3233/ifs-141205.

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5

Ahluwalia, Manu, and Larry Bull. "Coevolving functions in genetic programming." Journal of Systems Architecture 47, no. 7 (2001): 573–85. http://dx.doi.org/10.1016/s1383-7621(01)00016-9.

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6

Savage, Neil. "Using functions for easier programming." Communications of the ACM 61, no. 5 (2018): 29–30. http://dx.doi.org/10.1145/3193776.

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7

Alvarez, Fernando, and Nancy L. Stokey. "Dynamic Programming with Homogeneous Functions." Journal of Economic Theory 82, no. 1 (1998): 167–89. http://dx.doi.org/10.1006/jeth.1998.2431.

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8

Chou, J. H., Wei-Shen Hsia, and Tan-Yu Lee. "Convex programming with set functions." Rocky Mountain Journal of Mathematics 17, no. 3 (1987): 535–44. http://dx.doi.org/10.1216/rmj-1987-17-3-535.

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9

Wang, Chung-lie, and An-qing Xing. "Dynamic programming and penalty functions." Journal of Mathematical Analysis and Applications 150, no. 2 (1990): 562–73. http://dx.doi.org/10.1016/0022-247x(90)90123-w.

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10

Weir, T. "Programming with semilocally convex functions." Journal of Mathematical Analysis and Applications 168, no. 1 (1992): 1–12. http://dx.doi.org/10.1016/0022-247x(92)90185-g.

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11

Royset, J. O. "Optimality functions in stochastic programming." Mathematical Programming 135, no. 1-2 (2011): 293–321. http://dx.doi.org/10.1007/s10107-011-0453-3.

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12

Nigiyan, S. A. "$ \lambda $-DEFINABILITY OF BUILT-IN McCARTHY FUNCTIONS AS FUNCTIONS WITH INDETERMINATE VALUES OF ARGUMENTS." Proceedings of the YSU A: Physical and Mathematical Sciences 53, no. 3 (250) (2019): 191–202. http://dx.doi.org/10.46991/pysu:a/2019.53.3.191.

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The built-in functions of programming languages are functions with indeterminate values of arguments. The built-in McCarthy functions $ car $, $ cdr $, $ cons $, $ null $, $ atom $, $ if $, $ eq $, $ not $, $ and $, $ or $, are used in all functional programming languages. In this paper we show the $ \lambda $-definability of the built-in McCarthy functions as functions with indeterminate values of arguments. This result is necessary when translating typed functional programming languages into untyped functional programming languages.

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13

LACHHWANI, KAILASH. "FUZZY GOAL PROGRAMMING VS ORDINARY FUZZY PROGRAMMING APPROACH FOR MULTI OBJECTIVE PROGRAMMING PROBLEM." International Journal of Modern Physics: Conference Series 22 (January 2013): 757–61. http://dx.doi.org/10.1142/s2010194513010982.

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This paper presents the comparison between two solution methodologies Fuzzy Goal Programming (FGP) and ordinary Fuzzy Programming (FP) for multiobjective programming problem. Ordinary fuzzy programming approach is used to develop the solution algorithm for multiobjective functions which works for the minimization of the perpendicular distances between the parallel hyper planes at the optimum points of the objective functions. Suitable membership function is defined as the supremum perpendicular distance and a compromise optimum solution is obtained as a result of minimization of supremum perpendicular distance. Whereas, In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them and suitable membership function is defined for each objectives. Then achievement of the highest membership value of each of fuzzy goals is formulated by minimizing the negative deviational variables.

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14

Chadha, S. S. "Fractional programming with absolute-value functions." European Journal of Operational Research 141, no. 1 (2002): 233–38. http://dx.doi.org/10.1016/s0377-2217(01)00262-4.

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15

Junge, Oliver, and Alex Schreiber. "Dynamic programming using radial basis functions." Discrete & Continuous Dynamical Systems - A 35, no. 9 (2015): 4439–53. http://dx.doi.org/10.3934/dcds.2015.35.4439.

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16

Antczak, Tadeusz. "LIPSCHITZr-INVEX FUNCTIONS AND NONSMOOTH PROGRAMMING." Numerical Functional Analysis and Optimization 23, no. 3-4 (2002): 265–83. http://dx.doi.org/10.1081/nfa-120006693.

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17

Husain, Iqbal, Santosh K. Shrivastav, and Abdul Raoof Shah. "On Continuous Programming with Support Functions." Applied Mathematics 04, no. 10 (2013): 1441–49. http://dx.doi.org/10.4236/am.2013.410194.

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18

Mukherjee, R. N., and S. K. Mishra. "Multiobjective Programming with Semilocally Convex Functions." Journal of Mathematical Analysis and Applications 199, no. 2 (1996): 409–24. http://dx.doi.org/10.1006/jmaa.1996.0150.

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19

Mukherjee, R. N. "Generalized Pseudoconvex Functions and Multiobjective Programming." Journal of Mathematical Analysis and Applications 208, no. 1 (1997): 49–57. http://dx.doi.org/10.1006/jmaa.1997.5281.

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20

Feinberg, Brion. "Coercion Functions and Decentralized Linear Programming." Mathematics of Operations Research 14, no. 1 (1989): 177–87. http://dx.doi.org/10.1287/moor.14.1.177.

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21

Schechter, M. "Polyhedral functions and multiparametric linear programming." Journal of Optimization Theory and Applications 53, no. 2 (1987): 269–80. http://dx.doi.org/10.1007/bf00939219.

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22

van de Riet, R. P. "Logic programming functions, relations and equations." Future Generation Computer Systems 3, no. 3 (1987): 218–19. http://dx.doi.org/10.1016/0167-739x(87)90015-x.

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23

Prekopa, Andreas. "Stochastic programming with multiple objective functions." European Journal of Operational Research 27, no. 2 (1986): 260. http://dx.doi.org/10.1016/0377-2217(86)90078-0.

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24

Terlaky, T. "Smoothing empirical functions by lp programming." European Journal of Operational Research 27, no. 3 (1986): 343–63. http://dx.doi.org/10.1016/0377-2217(86)90331-0.

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25

Husain, I., Abha, and Z. Jabeen. "On nonlinear programming with support functions." Journal of Applied Mathematics and Computing 10, no. 1-2 (2002): 83–99. http://dx.doi.org/10.1007/bf02936208.

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26

Husain, I., and Z. Jabeen. "On fractional programming containing support functions." Journal of Applied Mathematics and Computing 18, no. 1-2 (2005): 361–76. http://dx.doi.org/10.1007/bf02936579.

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27

Choo, E. U., and K. P. Chew. "Optimal value functions in parametric programming." Zeitschrift für Operations Research 29, no. 1 (1985): 47–57. http://dx.doi.org/10.1007/bf01920495.

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28

CABALAR, PEDRO. "Functional answer set programming." Theory and Practice of Logic Programming 11, no. 2-3 (2011): 203–33. http://dx.doi.org/10.1017/s1471068410000517.

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AbstractIn this paper we propose an extension of Answer Set Programming (ASP) to deal with (possibly partial) evaluable functions. To this aim, we start from the most general logical counterpart of ASP, Quantified Equilibrium Logic (QEL), and propose a variant QEL=ℱwhere the set of functions is partitioned into Herbrand functions (orconstructors) and evaluable functions (oroperations). We show how this extension has a direct connection to Scott'sLogic of Existence, and introduce several useful derived operators, some of them directly borrowed from Scott's formalisation. Using this general framework for arbitrary theories, we proceed to focus on a syntactic subclass that corresponds to normal logic programs with evaluable functions and equality. We provide a translation of this class into function-free normal programs and consider a safety condition so that the resulting program is also safe, under the usual meaning in ASP. Finally, we also establish a formal comparison to Lin and Wang's approach (FASP) dealing with evaluable total functions.

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29

Chang, Ching-Ter. "Fractional programming with absolute-value functions: a fuzzy goal programming approach." Applied Mathematics and Computation 167, no. 1 (2005): 508–15. http://dx.doi.org/10.1016/j.amc.2004.07.014.

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30

Singh, Vishnu Pratap. "On Solving Linguistic Bi-Level Programming Problem Using Dynamic Programming." International Journal of Fuzzy System Applications 10, no. 1 (2021): 43–63. http://dx.doi.org/10.4018/ijfsa.2021010103.

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In this work, a linguistic bi-level programming problem has been developed where the functional relationship linking decision variables and the objective functions of the leader and the follower are not utterly well known to us. Because of the uncertainty in practical life decision-making situation most of the time, it is inconvenient to find the veracious relationship between the objective functions of leader, follower, and the decision variables. It is expected that the source of information which gives some command about the objective functions of leader and follower is composed by a block of fuzzy if-then rules. In order to analyze the model, a dynamic programming approach with a suitable fuzzy reasoning scheme is applied to calculate the deterministic functional relationship linking the decision variables and the objective functions of the leader as well as the follower. Thus, a bi-level programming problem is constructed from the actual fuzzy rule-based to the conventional bi-level programming problem. A numerical example has been solved to signify the computational procedure.

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31

Cai, Yongyang, Kenneth L. Judd, Thomas S. Lontzek, Valentina Michelangeli, and Che-Lin Su. "A NONLINEAR PROGRAMMING METHOD FOR DYNAMIC PROGRAMMING." Macroeconomic Dynamics 21, no. 2 (2016): 336–61. http://dx.doi.org/10.1017/s1365100515000528.

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A nonlinear programming formulation is introduced to solve infinite-horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to approximate value functions. Our numerical results show that this nonlinear programming is efficient and accurate, and avoids inefficient discretization.

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32

Zheng, Yingchun, and Xiaoyan Gao. "Sufficiency and Duality for Multiobjective Programming under New Invexity." Mathematical Problems in Engineering 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/8462602.

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A class of multiobjective programming problems including inequality constraints is considered. To this aim, some new concepts of generalizedF,P-type I andF,P-type II functions are introduced in the differentiable assumption by using the sublinear functionF. These new functions are used to establish and prove the sufficient optimality conditions for weak efficiency or efficiency of the multiobjective programming problems. Moreover, two kinds of dual models are formulated. The weak dual, strong dual, and strict converse dual results are obtained under the aforesaid functions.

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33

Lai, H. C., and J. C. Liu. "Minimax fractional programming involving generalised invex functions." ANZIAM Journal 44, no. 3 (2003): 339–54. http://dx.doi.org/10.1017/s1446181100008063.

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AbstractThe convexity assumptions for a minimax fractional programming problem of variational type are relaxed to those of a generalised invexity situation. Sufficient optimality conditions are established under some specific assumptions. Employing the existence of a solution for the minimax variational fractional problem, three dual models, the Wolfe type dual, the Mond-Weir type dual and a one parameter dual type, are constructed. Several duality theorems concerning weak, strong and strict converse duality under the framework of invexity are proved.

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34

Ivanov, Vsevolod Ivanov. "Second-order invex functions in nonlinear programming." Optimization 61, no. 5 (2012): 489–503. http://dx.doi.org/10.1080/02331934.2010.522711.

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35

Mishra, S. K., та B. B. Upadhyay. "Nonsmooth minimax fractional programming involvingη-pseudolinear functions". Optimization 63, № 5 (2012): 775–88. http://dx.doi.org/10.1080/02331934.2012.689833.

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36

Glover, B. M. "On Quasidifferentiable Functions and Non-Differentiable Programming." Optimization 24, no. 3-4 (1992): 253–68. http://dx.doi.org/10.1080/02331939208843794.

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37

Bector, C. R., S. Chandra, and V. Kumar. "Duality for minmax programming involvingV-invex functions." Optimization 30, no. 2 (1994): 93–103. http://dx.doi.org/10.1080/02331939408843974.

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38

Li, X. F., J. L. Dong, and Q. H. Liu. "Lipschitz B-Vex Functions and Nonsmooth Programming." Journal of Optimization Theory and Applications 93, no. 3 (1997): 557–74. http://dx.doi.org/10.1023/a:1022643129733.

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39

Sethuraman, Jay, Teo Chung Piaw, and Rakesh V. Vohra. "Integer Programming and Arrovian Social Welfare Functions." Mathematics of Operations Research 28, no. 2 (2003): 309–26. http://dx.doi.org/10.1287/moor.28.2.309.14478.

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40

Umnov, A. E., and E. A. Umnov. "Using Feedback Functions in Linear Programming Problems." Computational Mathematics and Mathematical Physics 59, no. 10 (2019): 1626–38. http://dx.doi.org/10.1134/s0965542519100142.

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41

KOSHI, Shozo, Hang Chin LAI, and Naoto KOMURO. "Convex programming on spaces of measurable functions." Hokkaido Mathematical Journal 14, no. 1 (1985): 75–84. http://dx.doi.org/10.14492/hokmj/1381757690.

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42

Nickel, Stefan, and Margaret M. Wiecek. "Multiple objective programming with piecewise linear functions." Journal of Multi-Criteria Decision Analysis 8, no. 6 (1999): 322–32. http://dx.doi.org/10.1002/1099-1360(199911)8:6<322::aid-mcda260>3.0.co;2-5.

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43

Köppe, Matthias, Christopher Thomas Ryan, and Maurice Queyranne. "Rational Generating Functions and Integer Programming Games." Operations Research 59, no. 6 (2011): 1445–60. http://dx.doi.org/10.1287/opre.1110.0964.

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44

Kharbanda, Pallavi, Divya Agarwal, and Deepa Sinha. "Non-differentiable multiobjective programming under generalised functions." International Journal of Operational Research 23, no. 3 (2015): 363. http://dx.doi.org/10.1504/ijor.2015.069627.

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45

Bai, Fu-sheng, Lian-sheng Zhang, and Zhi-you Wu. "General exact penalty functions in integer programming." Journal of Shanghai University (English Edition) 8, no. 1 (2004): 19–23. http://dx.doi.org/10.1007/s11741-004-0005-7.

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46

Broyden, C. G., and N. F. Attia. "Penalty functions, Newton's method, and quadratic programming." Journal of Optimization Theory and Applications 58, no. 3 (1988): 377–85. http://dx.doi.org/10.1007/bf00939388.

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47

Grimstad, Bjarne, and Brage R. Knudsen. "Mathematical programming formulations for piecewise polynomial functions." Journal of Global Optimization 77, no. 3 (2020): 455–86. http://dx.doi.org/10.1007/s10898-020-00881-4.

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48

Lai, H. C., J. C. Liu, and S. Schaible. "Complex Minimax Fractional Programming of Analytic Functions." Journal of Optimization Theory and Applications 137, no. 1 (2007): 171–84. http://dx.doi.org/10.1007/s10957-007-9332-8.

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49

Yu. Danilin, M. "Sequential quadratic programming and modified lagrange functions." Cybernetics and Systems Analysis 30, no. 5 (1994): 672–85. http://dx.doi.org/10.1007/bf02367748.

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50

Chang, Ching-Ter. "Multi-choice goal programming with utility functions." European Journal of Operational Research 215, no. 2 (2011): 439–45. http://dx.doi.org/10.1016/j.ejor.2011.06.041.

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