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How to verify (or proof) the following results of maximization and minimization problems?

Remark: $c$ should be positive since $y$ appears in the denominator. If $a \le x \le b$ and $c \le y \le d$, then we have $a \le x \le b$ and $\frac1d \le \frac1y \le \frac1c$ and hence $$\frac{a}{d}\...
Siong Thye Goh's user avatar
1 vote

Optimizing an Objective Function While Minimizing an Argument?

As a general optimization formulation, your problem can be written as, \begin{align} \min_{x_1, x_2} \; &x_2 \\ \text{s.t.} \; & f(x_1, x_2) = 0 \\ & x_1, x_2 \geq 0 \end{align} Most ...
Tony Mathew's user avatar
  • 2,382
1 vote

Finding the global minimum of a convex-like optimization problem

I would be very surprised if you could get anything beyond local minima in this general case without using (intractable) global optimization techniques. The class of quasiconvex functions are not ...
gabalz's user avatar
  • 316

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