Tagged Questions

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Combinations of Convex Functions

I'm looking at the following non-linear optimization theory problem: Let $\gamma$ be a monotone nondecreasing function of a single variable (that is, $\gamma(r) \le \gamma(r')$ for $r' > r$), ...
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Proofs involving closedness of compositions of mappings.

I've feel like I've gotten myself in over my head in a non-linear optimization course I seem to lack the mathematical maturity for(I'm an undergrad, I've taken the calc series, Intro to differential ...
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Conceptual Understanding of Non-Linear Optimization Problem

I'm in non-linear optimization, and I'm having trouble wrapping my head around what this problem is asking me for. If anyone could help with a conceptual explanation (not an answer!), it'd be greatly ...
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KKT minimization problem

Solve $x^2 - 2y \rightarrow \min$ subject to $\max\{3x^2, e^y + 2\} + \sqrt{x^2 + y^2 - 2x + 1} \leq 6x + \sqrt{5}$ and $\sqrt{x^2 + y^2 - 4x - 4y +8} -2x+2y \leq 0$ I tried computing the ...
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Solve the Lagrangian dual problem

Consider the (non-linear) optimization problem ($P$) $$max \quad3x_1 + 4x_2$$ $$s.t. \quad x_1^2 + x_2^2 \leq 25$$ $$\quad x_1,x_2 \geq 0$$ Solve the Lagrangian dual problem. I ...
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Formulate the Langrangian function of a non-linear optimization problem and solve it for $y\geq0$

Consider the (non-linear) optimization problem ($P$) $$max \quad3x_1 + 4x_2$$ $$s.t. \quad x_1^2 + x_2^2 \leq 25$$ $$\quad x_1,x_2 \geq 0$$ Formulate the Lagrangian function ...