{"id":30038,"date":"2020-02-04T23:04:05","date_gmt":"2020-02-04T20:04:05","guid":{"rendered":"http:\/\/ihcoedu.uobaghdad.edu.iq\/?p=30038"},"modified":"2020-02-05T10:54:12","modified_gmt":"2020-02-05T07:54:12","slug":"%d9%82%d8%b3%d9%85-%d8%a7%d9%84%d8%b1%d9%8a%d8%a7%d8%b6%d9%8a%d8%a7%d8%aa-%d9%8a%d9%86%d8%a7%d9%82%d8%b4-%d8%b1%d8%b3%d8%a7%d9%84%d8%a9-%d9%85%d8%a7%d8%ac%d8%b3%d8%aa%d9%8a%d8%b1-%d8%aa%d9%86%d8%a7","status":"publish","type":"post","link":"https:\/\/ihcoedu.uobaghdad.edu.iq\/?p=30038","title":{"rendered":"\u0642\u0633\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u064a\u0646\u0627\u0642\u0634 \u0631\u0633\u0627\u0644\u0629 \u0645\u0627\u062c\u0633\u062a\u064a\u0631 \u062a\u0646\u0627\u0642\u0634 \u0646\u062a\u0627\u0626\u062c \u0628\u0639\u0636 \u0627\u0646\u0648\u0627\u0639 \u0627\u0644\u062f\u0648\u0627\u0644 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u0628\u0629"},"content":{"rendered":"

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    \n
  • \n

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  • \n

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    \"\"\u00a0<\/span><\/h4>\n

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    \u00a0<\/span><\/h3>\n
    \n

    The main aim of this thesis is to introduce and study new types of non-convex sets (functions) which are considered as generalizations and extensions of ordinary convex set (functions) and other kinds of non-convex sets (functions) studied in literature.Some general and differentiability properties of the new established functions are discussed and proved. Some optimality properties for non-linear optimization problems involving the new non-convex functions as the objective functions and the new sets as constraints are studied. Different examples are presented to illustrate some of the new functions and show the relationships between them.<\/span><\/h3>\n

    \u00a0The first part of this thesis discusses the class of strongly – convex sets (functions) (respectively, semi strongly -convex, quasi semi strongly -convex, pseudo semi strongly -convex) functions.Some new properties of the aforementioned functions are presentedandsemi strongly -convex and quasi semi strongly -convex functions with their -level set are related. Moreover, some differentiability properties of strongly -convex, semi strongly -convex and quasi semi strongly -convex functions are shown. As an application of strongly -convexity to optimization problems, some optimality properties of non-linear constrained optimization problem in which the objective and\/or the constraints functions are strongly -convex, semi strongly -convex, strictly semi strongly -convex),\u00a0 quasi semi strongly -convex, and strictly quasi semi strongly -convex functions are discussed.<\/span><\/h3>\n

    The second part of this thesis deals with the class of -preinvex, – -preinvex, and local – -preinvex functions. Some properties of – -preinvex functions are discusses and some properties and characterizations of – -preinvex functions using -preinvex and -prequasiinvex functions are shown. Also, new results related to the invexity of different -level sets of – -preinvex functions are proved. Finally, some optimality properties of non-linear optimization problems for which the functions are local – -preinvex and – -preinvex functions and the constraint set is a local -invex setare discussed<\/span><\/h3>\n

    In the third part,the class of semi – -preinvex and pseudo – -preinvex functions are introduced with the study of different properties related to this class. Some necessary conditions for a function \u00a0to be semi – -preinvex using the level sets \u00a0and \u00a0and the epigraph of are provided. As in the first two parts, some optimality properties of non-linear optimization problems in which the objective function is semi – -preinvex, – -preinvex, and pseudo semi – -preinvex functions are studied.<\/span><\/h3>\n

    \u00a0<\/span><\/h4>\n","protected":false},"excerpt":{"rendered":"

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