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Analytic solution of low-dimensional Riccati equation
Consider the nonlinear map $F_i:\mathbb R^2 \to \mathbb R$
$F_i(x):=\varepsilon^2\langle x, A_i x\rangle +\varepsilon\langle b_i,x \rangle + x_i,$
where $A_i$ is some matrix and $b_i$ some vector
Can ...
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Analytic expression for the min value of $g(t):= \sqrt{(t-1)^2 + a^2}+ b|t|$ subject to $|t-1| \le c$
Disclaimer. Not sure this is MO-level but would really appreciate some help with this. Thanks in advance. Moved from SE.
Let $a,b,c \ge 0$, and define a function $g:\mathbb R \to \mathbb R$ by $g(t) :=...
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