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2018-09-27 21:45:10 +0200 | asked a question | solving an iterated optimization problem I have the following problem, which I intend to solve using SAGE. Given $m^2$ non-linear (smooth) functions $f_{ij}(x,y):[0,1]^2\rightarrow \mathbb{R}$, for $1\leq i,j \leq m$ I want to solve $$ \min_{x\in[0,1]} \max ( F_1(x), \ldots, F_m(x) )$$ where for any $1\leq i \leq m$: $$ F_i(x) = \min_{y\in [0,1]} \max ( f_{i1}(x,y), \ldots, f_{im}(x,y) )$$ I had thought of solving the inner Minimax problem $F_i(x)$ as a non-linear optimization problem with inequality constraints as $$\min z$$ $$ f_{ij}(x,y)-z \leq 0, \qquad 1\leq j \leq m$$ $$ y-1\leq 0 \qquad \mathrm{and} \qquad -y\leq 0$$ using the SAGE function sage.numerical.optimize.minimize_constrained. This works fine for a fixed value of $x$, but not in case $x$ is a free parameter. What I get is a TypeError: unable to simplify to float approximation For instance the following code
produces the error:
Does someone have an idea how to use minimize_constrained for functions with a free parameter? Are there other alternatives (except doing everything from scratch)? |