• Title/Summary/Keyword: support functions

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MULTIOBJECTIVE CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Ahmed, A.;Rumana, G. Mattoo
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.603-619
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    • 2009
  • Wolfe and Mond-Weir type dual to a nondifferentiable continuous programming containing support functions are formulated and duality is investigated for these two dual models under invexity and generalized invexity. A close relationship of our duality results with those of nondifferentiable nonlinear programming problem is also pointed out.

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CONTINUOUS PROGRAMMING CONTAINING SUPPORT FUNCTIONS

  • Husain, I.;Jabeen, Z.
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.75-106
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    • 2008
  • In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

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SECOND ORDER NONSMOOTH MULTIOBJECTIVE FRACTIONAL PROGRAMMING PROBLEM INVOLVING SUPPORT FUNCTIONS

  • Kharbanda, Pallavi;Agarwal, Divya;Sinha, Deepa
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.835-852
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    • 2013
  • In this paper, we have considered a class of constrained non-smooth multiobjective fractional programming problem involving support functions under generalized convexity. Also, second order Mond Weir type dual and Schaible type dual are discussed and various weak, strong and strict converse duality results are derived under generalized class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions. Also, we have illustrated through non-trivial examples that class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions extends the definitions of generalized convexity appeared in the literature.

A Kohn-nirenberg example using lower degree

  • Yi, Jeong-Seon
    • Communications of the Korean Mathematical Society
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    • v.11 no.1
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    • pp.81-87
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    • 1996
  • We will construct polynomials of degree 6 in z and $\bar{z}$ on $C^2$ which gives, via its coefficient $\beta$ as a parameter, a family of pseudoconvex domains $\Omega_\beta$ in $C^2$ with the origin being a boundary point, and show that the domains $\Omega_\beta$ has no peak functions of class $c^1$ at the origin and has no holomorphic support functions for $1 \leq \beta < \frac{9}{5}$.

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MIXED TYPE SECOND-ORDER DUALITY WITH SUPPORT FUNCTION

  • Husain, I.;Ahmed, A.;Masoodi, Mashoob
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1381-1395
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    • 2009
  • Mixed type second order dual to the non-differentiable problem containing support functions is formulated and duality theorems are proved under generalized second order convexity conditions. It is pointed out that the mixed type duality results already reported in the literature are the special cases of our results.

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Requirement Analysis and Optimal Design of an Operational Change Detection Software

  • Lee, Young-Ran;Bang, Ki-In;Shin, Dong-Seok;Jeong, Soo;Kim, Kyung-Ok
    • Korean Journal of Remote Sensing
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    • v.20 no.3
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    • pp.189-196
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    • 2004
  • This paper describes what an operational change detection tool requires and the software which was designed and developed according to the requirements. The top requirement for the application of the software to operational change detection was identified: minimization of false detections, missing detections and operational cost. In order to meet such a requirement, the software was designed with the concept that the ultimate decision and isolation of changes must be performed manually by visual interpretation and all automatic algorithms and/or visualization techniques must be defined as support functions. In addition, the modular structure of the proposed software enables the addition of a new support function with the minimum development cost and minimum change of the operational environment.

Relationships between Maternal support network and perceptions of parenting task difficulty (어머니의 자녀양육에 대한 사회적 관계망과 양육곤란도 지각과의 관계)

  • Rhee, Un Hai;Lee, Mee Ry
    • Korean Journal of Child Studies
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    • v.17 no.2
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    • pp.61-78
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    • 1996
  • The purpose of this study was to describe maternal social networks and to examine their relationships to maternal perceptions of parenting task difficulty. One hundred and thirty-three mothers of preschool children responded to a questionnaire indicating individuals in their networks, support functions, and perceptions of task difficulty. Mothers reported an average of 6.5 persons in their networks, including primarily with her own mother, the husband, mother-in-law, and sisters. While support was provided mainly by her husband and her own family members, the kinds of support varied depending on the person in networks. It was also found that support functions were different in terms of maternal job status, sex of the child, and the child's previous experience in day care or early childhood education settings. Emotional support from networks was significantly related to parenting task difficulty, especially in daily routine care. Mothers who perceived more emotional support from networks reported parenting to be less difficult.

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ON OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL OPTIMIZATION PROBLEMS

  • Kim, Moon-Hee;Kim, Gwi-Soo
    • Communications of the Korean Mathematical Society
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    • v.25 no.1
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    • pp.139-147
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    • 2010
  • A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

OPTIMALITY CONDITIONS AND DUALITY IN NONDIFFERENTIABLE ROBUST OPTIMIZATION PROBLEMS

  • Kim, Moon Hee
    • East Asian mathematical journal
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    • v.31 no.3
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    • pp.371-377
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    • 2015
  • We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functions and support functions as its objective function, continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.

A study on the development of CAM system for turning (선삭가공용 CAM 시스템의 개발에 관한 연구)

  • 양민양;이성찬;최종률;강성균
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.529-533
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    • 1996
  • Recently, manufacturing industries are doing their best to increase productivity and to reduce production time. One of tile efforts is to develop user-friendly and effective CAM systems. For this purpose, a CAM system for turning was developed. In the developed system. user interacts with tile CAM system using graphical user interface (GUI) and manufacturing support functions to make NC programs effectively. Manufacturing support functions include cycle decoder. interference check be ween tool and workpicce. bar turning without air cut and dynamic/wireframe simulation. In the cycle decoder. basic options are provided to novices for their convenience. and advanced options are provided to help expert to modify the program using their knowledge. Interference check has been nil issue in tile CAM system for tuning. In this paper. when a user selects a tool. interference check between selected tools and workpieces is done automatically. Moreover. remaining shapes are calculated automatically. Then, tile CAM system requests user to input all additional tool and generates NC codes to cut tile remaining shapes. In bar turning of forged raw material, air cut should be prevented for effective machining. For this purpose, a new algorithm for bar turning was developed. Dynamic and wireframe simulation was used to verify the generated NC code.

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