The ma j or theme of this thesis is nonlinear programming with an em - phasis on
.... of continuous nonlinear programming provides some theory and algorithms.
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JLK.MON PRQTSU0VWMXJMYSZ\[]N ^
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Rc jld pq_hg
Rqc q _h_hg&)l
jgutr~gq_hb)c4Wc jllc blefefr~gq0jl
Rz d m6jwq_hu~z4blg `` u~r~sab)d rxjgz pqc{r~z d jT_acc{jeH}wr
s pqc{r~z d jT_acc{jeH}wrTR)l jd jlc{z b }pRblgu~r~gb)c4}r~&4pblu~eC_ac{zd _wgr~z*bCpjl zlju~b 0z _ac{rx_gc ll ! " _a` b)c d eC_hgdjlkWm&b)d pq_heIb)d r~sabluvwsar~_hgsy_hz r~}r~z{rxjgjlkmob)d pq_hefb)d r~saz pblu~eC_ac z|grx}l_ac z rxdjlk _hs pgqjuxjll6blg&|gr~}l_ac{z rxd Ijlkjld pq_hg
Rqc w# $%hf & jl d _a
jlc _h_hg _hux_a` pqjgq( _ ') +* ,- &). all
Wc{r~gd _hb)dd pq__a`Rb)c{d eC_hgidjlkWm&b)d pq_heIb)d r~sabluvwsar~_hgsy_hz jl d _a
jlc qT_hq_hg&)l &
!#"$%'& (!) *& +-,, ./ 0"1 ! JLK.MON PRQTSU0VWMXJMYSZ\[]N ^ _a`Rb)c d ef_hgidjlknmob)d pq_hefb)d rtsabluvwsarx_hgRsy_hz pbluteC_ac{z4|grx}l_ac{z r~djlkv _hs{pgjuxjll blg&|gr~}l_ac{z rxd jlkWjld pq_hg
Rqc
2346587:9 jlcd pq_hef_fjlkd pr~z d pq_hz{r~zr~z gqjgRu~r~gq_hb)c `c{jllc{blefefr~grxd p blgB_he `Rpblz r~zjg b)``Ru~rtsab)d rxjgz blg c{jl
Rz deCjwq_hu~zA@Ipq_fd p_hz r~zpblzHdj&`Rb)c{d z6@ p_ B c{z dd pqc _a_`Rb)`_ac{zsyjeC`c{rtz _d pq_ B c{z d`Rb)c d6@W_ac _lq_Rr~z saz z c jl
RRz d gq_hz z`c jl`% _ac d rx_hzjlkHjl`d rtefbluz ju~qd rxjgRz d j b })b)c{rx_ad jlk]efjq_hut6z @ pq_ B c{z d d j ` b)`T_ac z syjgsy_ac{g jl`d r~eIDr Chb)d rxjg eCjwq_hu~) z gj g blz]d jws{pRblz d r~sCm&b)d p_hefb)d r~sabluWc jllc{blefz rxd pF Er~utrx
c{r~Re jgz d c{blr~gd z * qmo ,G@Rpq_hz _Hb)c _Hz d jws{pRblz d r~sjl`Rd r~efDr Chb)d rxjg `c jl
Rux_heIzOd pb)dnpb }l_4dju~_a}l_hu~zvjl'k H q_hsar~z{rxjgJz ILK buxj _ac ux_a}l_huwjgq_blg.blg ``_ac ux_a}l_huTjgq=_ @pq_ uxj _ac ux_a}l_hu`c jl
Ru~_he rtzrtg d p_k jlc{eXjlkvb]})b)c{r~b)d r~jgblur~gqA_ Eblu~rxd l blgId p_q`R`T_ac ux_a}l_hujlL
> _hsyd rx}l_k gsyd rxjgr~z _hrxd pq_acd pq_N_ Mw`_hsyd _h0}*blutq_ jlk blgjl
> _hsyd rx}l_ jlc4d p_jgrxd rxjgRbl _hsyd r~}l_&N_ Mwd _hgz rxjgzIjlk d pq_ qmoXk c{bleC_ajlc /@ pq_&z d b)
Rrtu~rxd jlkjl`d r~efblu z ju~qd rxjgRz q_Cd j&s pblgql_hzHrtg d pq_IgRq_ac{uxwr~gq `c jl
Rb)
Rrtu~rxdor~z d c{r~
Rqd rxjg r~zblgb ux Ca_h0 @PQ _Cblu~z jI`c _hz _hgiddjb)`` u~r~sab)d rxjgzd jll_ad pq_ac rxd p&geC_ac r~sabluON_ MqbleC`Rux_hAz K gd _hgz rxd .m&jwu~b)d _h blr~b)d r~jgfpq_ac{b)`. * mo ,nblgId c{#b SIsg_adjlc fq_hz rx0g @ g.d p_4d prxc{ `Rb)`_achl_syjgz r~_acWb gqjgu~r~g_hb)cv`Rc jllc{ble r~d p e uxd r~`Rux_jlL
> _hs d rx}l_hz4 prts{p6b)c _]z qL
> _hsyd _hd jIgRsy_ac d blr~gdr~g0d pq_})b)c{r~b)
ux_hz4blg6r~g6d pq_ `Rb)c{ble _ad _ac{6z @_ac _H_ jIgqjldRz _]b z d js pblz d r~s]`c jllc blefefr~gqfb)`R`c jbls{pO
Rd r~gz d _hbl _r~z p.d j]blgRblux Ca_ c jl
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Rz d g_hz zjlk jl`Rd r~efbluOz j u~qd rxjgAz @ pr~z4r~z4blsasyjeC` u~r~z pq_h0d pc jqpd pq_]syjgz d c{syd r~jgjlknbfqd r~u~r~dIk gsyd r~jg pr~s p0c _hsy_hz4d p_e]u~d r jlL
> _hsyd rx}l_ `c jl
Ru~_he r~gid j bCz r~gqux_ jlT
> _hsyd rx}l_H`c jl
Rux_hU e @ pq_fz _hsyjgR `Rb)c d jlkd pq_Cd pq_hz{r~za syjlc c{_hz `jgr~gq0d j6d p_Ck jqc{d p `Rb)`_ach syjg sy_ac{gz d pq_`c jl
ux_he jlkgReC_ac{r~sablu~u~ k ju~Rr~gqoblgblr~c
Rb)T @Q _6b)`R`c Aj Mqr~efb)d _0d pq_ r~r~r
blrxc
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b ERblz r sywu~r~gqc r~sabluh`juxwpq_hqc jgOhblg _z pqj pqj , c{rxblefr efb)d pq_hefb)d r~saz sablg
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Rux_her~z z jux}l_h.d pqc jqp d pq_k jlc{e u~b)d rxjg]jlk b gjgu~r~gq_hb)c `c jllc{bleXpqjz _jl`d r~efbluTz ju~d rxjg0syjlc c _hz `jgz d jCd pq_ syjjlc{r~gb)d _hz jlkOd pq_}l_ac d r~sy_hzjlk d pq_ b)d d _hgq_h`juxwpq_hqc j0g @vp_eC_ad pqjwr~z _heCjgz d c{b)d _h0jg bCsyjeC`Rqd _aceCj_hujlkvbC` blz z _hgql_ac blr~c
Rb)T@
7 4 jl`d r~eIDr Chb)d rxjgYqc jl
z d gq_hz zhwe uxd r jlL
> _hsyd r~}l_jl`d r~efr Chb)d rxjgY z d js pblz d r~sefb)d pq_heIb)d r~sabluR`Rc jllc{blefz rxd pI_AErtu~rx
c{rte syjgRz d c{blr~gd zawsyjgrxd rxjgRblu }*blu~_ b)d- c{r~z Tq mo qd c{b#SIsHgq_adjlc6q_hz r~gYqblrxc
Rb)Ck ju~r~gq c{rxblefr
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9 7 c je]}wr @blgLb)d c{r z z jgYm)@
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