Az eredeti feladat

S = 49 ; T = 59 ; τ = 0.2 ; Overscript[u, _] = 0.466 ;

σ  abszolút értékben kisebb, mint 1?

w[x_, σ_: - 0.5, θ_:4.1] := θ + x^σ/σ ; f[t_] := 1/(T - S + 1) (*most állandó ? *) ; ψ[v_, ρ_: - 1] := v^ρ/ρ(*ρ = -1 vagy 1 ? *)

Solve[Overscript[u, _] - w[b^*] + w '[b^*] (τ + b^*) == 0, b^*]

{{b^* →0.799851}}

ClearAll[R, r, B, b, V, v, F] ;

R = Array[r_#&, T - S + 1, S] ;

b = Array[B_#&, T - S + 1, S] ;

v = Array[V_#&, T - S + 1, S] ;

F = Array[f[#] &, T - S + 1, S] ;

R

{r_49, r_50}

b

{B_49, B_50}

v

{V_49, V_50}

F

{1/2, 1/2}

elso = Thread[v == (Overscript[u, _] - w/@b) R + (w/@b) Range[S, T]]

{V_49 == 49 (4.1 - 2./B_49^0.5) + (-3.634 + 2./B_49^0.5) r_49, V_50 == 50 (4.1 - 2./B_50^0.5) + (-3.634 + 2./B_50^0.5) r_50}

masod = ((τ + b) R - Range[S, T] b) . F == 0

1/2 (-49 B_49 + (0.2 + B_49) r_49) + 1/2 (-50 B_50 + (0.2 + B_50) r_50) == 0

harmad = Thread[Most[RotateLeft[v]] == Most[v] + w/@Most[b]]

{V_50 == 4.1 - 2./B_49^0.5 + V_49}

pozitivak = Join[Thread[b>0], Thread[R>0]]

celfv = (ψ/@v) . F

-1/(11 V_49) - 1/(11 V_50) - 1/(11 V_51) - 1/(11 V_52) - 1/(11 V_53) - 1/(11 V_54) - 1/(11 V_55) - 1/(11 V_56) - 1/(11 V_57) - 1/(11 V_58) - 1/(11 V_59)

NMaximize[{celfv, elso, masod, harmad}, Join[b, R, v]]

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