# Questions tagged [numerical-optimization]

Numerical methods for continuous optimization.

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### How to formulate piecewise quadratic function optimization without introducing binary variables?

I have a problem with logical constraints (either-or constraints). I know that it can be solved by either big-M or complementary formulations. However, i do not want to convert it into mixed-integer ...
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### bound for SR1 update

Suppose the exact hessian $H^\star$ as function of vector x (no need to further be specified) and the initial SR-1 approximation $H$ are globally bounded in some norm of your choice by some real ...
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### Challenges with a Multi-label Regression Problem in a Real Estate Dataset

I am currently conducting a research where I aim to predict the selling price and deal execution time of properties in NY. To do this, I have a dataset of various properties sold in NY, containing ...
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### What's the purpose of the KKT condition when first-order optimality condition exists?

Given a convex optimization problem $$\min f(x), x \in D$$ $f, D$ convex. The first-order optimality condition says $x$ is the minimizer if and only if $\nabla f(x)^T (x-y) \geq 0, \forall y\in D.$ ...
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### Solving a convex problem with quasiconvexity with CVXPY?

I have a question regarding quasiconvexity and its usage in CVXPY. I have the following optimization problem. \begin{equation*} \begin{aligned} \min_{x} \quad & \sqrt x\\ \textrm{subject to:} \...
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### Brachistochrone involving gravitational changes dependent on x

as an extension to the normal brachistochrone problem: $$T[y]=F(y,y')= \tfrac{1}{\sqrt{2g}}\int_{0}^{x_{b}}\tfrac{\sqrt{1+(y'(x))^2}}{\sqrt{y(x)}}dx$$ I was asked to get the gravity dependent on x, so ...
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### Gradient-based methods on quasi-convex problems?

In the book I am currently reading, it says Gradient-based methods are useful for one global optimum and no additional local optima: (quasi-)concave for maximums, (quasi-)convex for minimums. It is ...
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### IN SVMs, why can't the Lagrange multipliers for support vectors be 0?

In hard margin SVMs, we have the primal optimization problem: \begin{align*} \min_{\vec{w}, b} \max_{\vec{\alpha}} \quad & \frac{||\vec{w}||^2}{2} + \sum_{i=1}^m \alpha_i \left( 1 - y_i (\vec{w} \...
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