Separable Programming: Theory and Methods
S.M. Stefanov
11.2013β―Π³. Β· Applied Optimization ΠΠ½ΠΈΠ³Π° 53 Β· Springer Science & Business Media
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
314
Π‘ΡΡΠ°Π½ΠΈΡΠΈ
reportΠΡΠ΅Π½ΠΊΠΈΡΠ΅ ΠΈ ΠΎΡΠ·ΠΈΠ²ΠΈΡΠ΅ Π½Π΅ ΡΠ° ΠΏΠΎΡΠ²ΡΡΠ΄Π΅Π½ΠΈ Β ΠΠ°ΡΡΠ΅ΡΠ΅ ΠΏΠΎΠ²Π΅ΡΠ΅
ΠΡΠΈΡΠΊΠΎ Π·Π° ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming. Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered.
Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed.
As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well.
Audience: Advanced undergraduate and graduate students, mathematical programming/ operations research specialists.
Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed.
As an application, these algorithms are used in the implementation of stochastic quasigradient methods to some separable stochastic programs. Numerical approximation with respect to I1 and I4 norms, as a convex separable nonsmooth unconstrained minimization problem, is considered as well.
Audience: Advanced undergraduate and graduate students, mathematical programming/ operations research specialists.
ΠΡΠ΅Π½Π΅ΡΠ΅ ΡΠ°Π·ΠΈ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½Π° ΠΊΠ½ΠΈΠ³Π°
ΠΠ°ΠΆΠ΅ΡΠ΅ Π½ΠΈ ΠΊΠ°ΠΊΠ²ΠΎ ΠΌΠΈΡΠ»ΠΈΡΠ΅.
ΠΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡ Π·Π° ΡΠ΅ΡΠ΅Π½Π΅ΡΠΎ
Π‘ΠΌΠ°ΡΡΡΠΎΠ½ΠΈ ΠΈ ΡΠ°Π±Π»Π΅ΡΠΈ
ΠΠ½ΡΡΠ°Π»ΠΈΡΠ°ΠΉΡΠ΅ ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ΡΠΎ Google Play ΠΠ½ΠΈΠ³ΠΈ Π·Π° Android ΠΈ iPad/iPhone. Π’ΠΎ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ½ΠΎ ΡΠ΅ ΡΠΈΠ½Ρ
ΡΠΎΠ½ΠΈΠ·ΠΈΡΠ° Ρ ΠΏΡΠΎΡΠΈΠ»Π° Π²ΠΈ ΠΈ Π²ΠΈ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ²Π° Π΄Π° ΡΠ΅ΡΠ΅ΡΠ΅ ΠΎΠ½Π»Π°ΠΉΠ½ ΠΈΠ»ΠΈ ΠΎΡΠ»Π°ΠΉΠ½, ΠΊΡΠ΄Π΅ΡΠΎ ΠΈ Π΄Π° ΡΡΠ΅.
ΠΠ°ΠΏΡΠΎΠΏΠΈ ΠΈ ΠΊΠΎΠΌΠΏΡΡΡΠΈ
ΠΠΎΠΆΠ΅ΡΠ΅ Π΄Π° ΡΠ»ΡΡΠ°ΡΠ΅ Π·Π°ΠΊΡΠΏΠ΅Π½ΠΈΡΠ΅ ΠΎΡ Google Play Π°ΡΠ΄ΠΈΠΎΠΊΠ½ΠΈΠ³ΠΈ ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²ΠΎΠΌ ΡΠ΅Π± Π±ΡΠ°ΡΠ·ΡΡΠ° Π½Π° ΠΊΠΎΠΌΠΏΡΡΡΡΠ° ΡΠΈ.
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈ ΡΠ΅ΡΡΠΈ ΠΈ Π΄ΡΡΠ³ΠΈ ΡΡΡΡΠΎΠΉΡΡΠ²Π°
ΠΠ° Π΄Π° ΡΠ΅ΡΠ΅ΡΠ΅ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²Π° Ρ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎ ΠΌΠ°ΡΡΠΈΠ»ΠΎ, ΠΊΠ°ΡΠΎ Π½Π°ΠΏΡΠΈΠΌΠ΅Ρ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈΡΠ΅ ΡΠ΅ΡΡΠΈ ΠΎΡ Kobo, ΡΡΡΠ±Π²Π° Π΄Π° ΠΈΠ·ΡΠ΅Π³Π»ΠΈΡΠ΅ ΡΠ°ΠΉΠ» ΠΈ Π΄Π° Π³ΠΎ ΠΏΡΠ΅Ρ
Π²ΡΡΠ»ΠΈΡΠ΅ Π½Π° ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎΡΠΎ ΡΠΈ. ΠΠ·ΠΏΡΠ»Π½Π΅ΡΠ΅ ΠΏΠΎΠ΄ΡΠΎΠ±Π½ΠΈΡΠ΅ ΠΈΠ½ΡΡΡΡΠΊΡΠΈΠΈ Π² ΠΠΎΠΌΠΎΡΠ½ΠΈΡ ΡΠ΅Π½ΡΡΡ, Π·Π° Π΄Π° ΠΏΡΠ΅Ρ
Π²ΡΡΠ»ΠΈΡΠ΅ ΡΠ°ΠΉΠ»ΠΎΠ²Π΅ΡΠ΅ Π² ΠΏΠΎΠ΄Π΄ΡΡΠΆΠ°Π½ΠΈΡΠ΅ Π΅Π»Π΅ΠΊΡΡΠΎΠ½Π½ΠΈ ΡΠ΅ΡΡΠΈ.
