33218

منظم سازي به روش شبه معين

كارشناسي ارشد

رياضي

1393

1393/08/10

دكتر بتول جذبي

ندارم

رياضي

ﺑﺮﻧﺎﻣﻪ رﯾﺰي ﺷﺒﻪ ﻣﻌﯿﻦ ﮔﺮوه ﻣﻬﻤﯽ از ﺑﺮﻧﺎﻣﻪ رﯾﺰي ﻣﺨﺮوﻃﯽ اﺳﺖ ﮐﻪ ﯾﮏ اﺑﺰار ﻣﻬﻢ در ﻣﺪﻟﺴﺎزي اﺳﺖ و ﮐﺎرﺑﺮدﻫﺎي زﯾﺎدي دارد ﻋﻼوه ﺑﺮ ﻗﺪرت ﻣﺪﻟﺴﺎزي ﻗﺎﺑﻠﯿﺖ ﻣﻬﻢ آن در در ﺣﻞ ﺗﺌﻮرﯾﮏ و ﻋﻤﻠﯽ ﯾﮑﯽ دﯾﮕﺮ از ﻋﻠﻞ ﮐﺎرﺑﺮد وﺳﯿﻊ اﯾﻦ روش ﻣﺪﻟﺴﺎزي اﺳﺖ .در ﺣﺎل ﺣﺎﺿﺮ ﻣﺤﺒﻮﺑﺘﺮﯾﻦ اﻟﮕﻮرﯾﺘﻢ ﺣﻞ در ﻣﺪل SDP روش ﻫﺎي ﻧﻘﻄﻪ دروﻧﯽ اﺳﺖ 101].،65،[3ﻧﺮم اﻓﺰارﻫﺎﯾﯽ ﻣﺜﻞ 3 [92]SDPT، [10]DSDP، 16]CSDP،[15،[85]SeDeMi وﺧﺎﻧﻮاده SDPAﻫﺎ ﻣﺜﻞ 100]،43،[42 MOSEKاز اوﻟﯿﻦ ﻧﺮم اﻓﺰارﻫﺎي ﺗﺠﺎري ﺣﻞ ﮐﻨﻨﺪه SDP ﻫﺴﺘﻨﺪ.در اﮐﺜﺮﯾﺖ روش ﻫﺎي ﻧﻘﻄﻪ دروﻧﯽ ﻧﺘﺎﯾﺞ ﺣﺎﺻﻞ از ﻫﻤﮕﺮاﯾﯽ ﺗﺌﻮرﯾﮏ ﺑﺮ اﺳﺎس اﯾﻦ ﻓﺮﺿﯿﻪ ﻫﺴﺘﻨﺪ ﮐﻪ SDP و دوﮔﺎﻧﺶ در ﺷﺮاﯾﻂ اﮐﯿﺪا ﺷﺪﻧﯽ )ﯾﺎ ﺷﺮاﯾﻂ اﺳﻼﺗﺮ( ﺻﺪق ﻣﯿﮑﻨﻨﺪ و اﯾﻦ ﻣﻄﻠﺐ اﺳﺖ ﮐﻪ ﺧﻮش ﺗﻌﺮﯾﻔﯽ ﻣﺴﯿﺮ ﻣﺮﮐﺰي را ﺗﺴﻬﯿﻞ ﻣﯽ ﻧﻤﺎﯾﺪ.اﻟﺒﺘﻪ از ﻃﺮف دﯾﮕﺮ ﺗﻌﺪادﮐﻤﯽ ازاﻟﮕﻮرﯾﺘﻢ ﻫﺎي دﯾﮕﺮ ﻫﻢ ﻣﻮﺟﻮد اﺳﺖ ﮐﻪ ﻫﻤﮕﺮاﯾﯽ ﺗﺤﻠﯿﻠﯽ آﻧﻬﺎ ﺑﺪون ﺑﺮﻗﺮار ﺑﻮدن ﺷﺮط ﺷﺪﻧﯽ اﮐﯿﺪ ﺗﺎﻣﯿﻦ ﻣﯿﺸﻮد[39]در ﻋﻤﻞ ﺿﺮورﺗﯽ ﻧﺪارد ﮐﻪ ﺣﺘﻤﺎ ﯾﮏ sdp اﮐﯿﺪا ﺷﺪﻧﯽ ﺑﺎﺷﺪ و در ﻣﻮاﻗﻌﯽ ﮐﻪ ﻣﺴﺌﻠﻪ ﻣﺎ در ﺷﺮط اﮐﯿﺪا ﺷﺪﻧﯽ ﺻﺪق ﻧﻤﯽ ﮐﻨﺪ ﯾﮏ راه ﻓﺮﻣﻮل ﺑﻨﺪي دوﺑﺎره ﻣﺴﺌﻠﻪ و رﺳﯿﺪن ﺑﻪ ﯾﮏ ﻣﺪل ﺟﺪﯾﺪ اﺳﺖ ﮐﻪ ﺧﻮدش و دوﮔﺎﻧﺶ اﮐﯿﺪا ﺷﺪﻧﯽ ﻫﺴﺘﻨﺪ.ﺳﭙﺲ ﺑﺎ اﺳﺘﻔﺎده از اﻟﮕﻮرﯾﺘﻢ ﻫﺎي ﻧﻘﻄﻪ دروﻧﯽ ﺑﻪ ﺣﻞ ﻣﺪل ﺟﺪﯾﺪ ﺣﺎﺻﻠﻪ ﻣﯽ ﭘﺮدازﯾﻢ.

1404/01/20

regularization in semidefinite programming

1/1/1900 12:00:00 AM

In this thesis the cubic semiorthogonal compactly supported B-spline wavelets with their boundary wavelets as a basis functions are used to solve the non- linear Fredholm–Hammerstein integral equations. In chapter 1,some required definitions and theorems are presented. In chapter 2, a brief history and definition of integral equations are expressed. In chapter 3,wavelet theory and MRA analysis are described completley.scince cubic B-spline are semi orthogonal so we need B-orthogonal MRA which is introduced in this chap- ter. In chapter 4 cubic B-spline wavelets with their properties and bound- ary wavelets are described. In chapter 5,the semi orthogonal cubic B-Spline wavelets with their dual wavelets are developed to approximate the solution of nonlinear Fredholm-Hammerstein integral equations.actually we reduce the integral equations to algebraic system which can be solved easily.at the end of this chapter some numerical examples are illustrated.

مسئله افراز گراف , قضيه پايولار

graph partitioninig

narges gorji

dr batool jazbi