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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

Turner, D. "Total Functional Programming." JUCS - Journal of Universal Computer Science 10, no. (7) (2004): 751–68. https://doi.org/10.3217/jucs-010-07-0751.

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The driving idea of functional programming is to make programming more closely related to mathematics. A program in a functional language such as Haskell or Miranda consists of equations which are both computation rules and a basis for simple algebraic reasoning about the functions and data structures they define. The existing model of functional programming, although elegant and powerful, is compromised to a greater extent than is commonly recognised by the presence of partial functions. We consider a simple discipline of total functional programming designed to exclude the possibility of non
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3

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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4

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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5

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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6

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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7

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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8

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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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

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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13

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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14

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 perpe
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15

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 fram
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16

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
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17

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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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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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31

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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32

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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33

Tasoluk, Berker, and Zuhal Tanrikulu. "The Performance Comparison of a Brute-Force Password Cracking Algorithm using Regular Functions and Generator Functions in Python." International Journal of Security, Privacy and Trust Management 12, no. 2 (2023): 01–06. http://dx.doi.org/10.5121/ijsptm.2023.12201.

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Python is used extensively in research, including algorithm testing. Python is a multi-paradigm programming language and supports both object-oriented programming and functional programming. In the functional side, it supports both regular functions and generator functions. This study tests both approaches in terms of usability cases and performance. A password-cracking algorithm is used for this tryout.
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34

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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35

CHANG, CHING-TER. "EFFICIENT STRUCTURES OF ACHIEVEMENT FUNCTIONS FOR GOAL PROGRAMMING MODELS." Asia-Pacific Journal of Operational Research 24, no. 06 (2007): 755–64. http://dx.doi.org/10.1142/s0217595907001516.

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Following the idea of Li (1996), Romero (2004) and Chang (2006), this paper proposes several efficient structures of achievement functions for goal programming and interval goal programming models. These proposed structures of achievement functions are more efficient than the traditional structures of achievement functions such as Lexicographic, Weight, MINMAX (Chebyshev) and interval achievement functions. The structures of achievement functions are comprehensive in terms of the breath of goal programming and interval goal programming. In order to demonstrate the superiority of the proposed m
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36

لايذ, واثق حياوي. "Decisions making for fraction functions By Using Goal Programming Method." Journal of Engineering 18, no. 08 (2023): 151–59. http://dx.doi.org/10.31026/j.eng.2012.08.01.

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Decision making is vital and important activity in field operations research ,engineering ,administration science and economic science with any industrial or service company or organization because the core of management process as well as improve him performance . The research includes decision making process when the objective function is fraction function and solve models fraction programming by using some fraction programming methods and using goal programming method aid programming ( win QSB )and the results explain the effect use the goal programming method in decision making process whe
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37

Horváth, Zoltán, Zoltán Porkoláb, Dániel Balázs Rátai, and Melinda Tóth. "Cell-oriented programming." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 56 (2024): 227–47. https://doi.org/10.71352/ac.56.227.

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In the currently existing distributed architectures, there are different components that are optimized to fulfill different roles (e.g. databases, message brokers, load-balancers) in the whole architecture. Distributed architectures are highly complex. Several competencies are needed to be able to create and maintain such an environment. Furthermore, these systems have strict limitations in performance optimization as well because the interaction between the components is limited to their interfaces. The Object-oriented programming (OOP) paradigm uses encapsulation to bind together the data an
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38

Bonelli, Nicola, Fabio Del Vigna, Alessandra Fais, Giuseppe Lettieri, and Gregorio Procissi. "Programming socket-independent network functions with nethuns." ACM SIGCOMM Computer Communication Review 52, no. 2 (2022): 35–48. http://dx.doi.org/10.1145/3544912.3544917.

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Software data planes running on commodity servers are very popular in real deployments. However, to attain top class performance, the software approach requires the adoption of accelerated network I/O frameworks, each of them characterized by its own programming model and API. As a result, network applications are often closely tied to the underlying technology, with obvious issues of portability over different systems. This is especially true in cloud scenarios where different I/O frameworks could be installed depending on the configuration of the physical servers in the infrastructure. The n
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39

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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40

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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41

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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42

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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43

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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44

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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45

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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46

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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47

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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48

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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49

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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50

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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