# Questions tagged [numerical-optimization]

Numerical methods for continuous optimization.

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### stochastic subgradient descent

When using stochastic subgradient descent, the solution $f_{best}(x_k)= \min \{f(x_1),f(x_2),....f(x_k) \}$, i.e., the best "point" over all the steps. As I understand, I should evaluate the function ...
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### Learn Numerical methods in Python

Please suggest me some texts that I could use to learn Numerical Methods in Python (irrespective of 2.7 or 3.x). I would like to improve my coding skills with Python along with refreshing my math in ...
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### Scaling/nondimensionalization for numerical optimization

I have a numerical optimization problem that I am trying to scale appropriately, in order to allow for the solver to achieve faster and more accurate results. I found a paper here that had a short ...
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### Writing an accurate SDP solver in Matlab

As part of a research project I'm supposed to write an semidefinite programming solver in Matlab (similar to SDTP3, MOSEK, SEDUM, etc) except it needs to be able to solve to many significant digits ...
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### How to solve this optimization problem analytically (parameter selection problem)?

My problem is as follows: \begin{align} \underset{\boldsymbol{x}}\max \quad & \boldsymbol r^T\boldsymbol x-\boldsymbol t^T\boldsymbol x \\ \text{s.t.} \quad & \boldsymbol1^T\boldsymbol x = N \...
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### Minimizing sum of two functions, minimize one and maximize the other.

I'm new in optimization and I have a problem involving minimizing the sum of two functions f(x) and g(x). The objective function must be in such a way that f(x) has to be minimized and g(x) maximized, ...
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### A nonlinear optimization problem: numerical solution fails

I am working on a practical problem which requires a theoretical analysis. Specifically, the problem is: Given a list of items, each enclosed in a rectangular box and with a given weight, and given ...
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### How to show that the method of steepest descent does not converge in a finite number of steps?

I have a function, $$f(\mathbf{x})=x_1^2+4x_2^2-4x_1-8x_2,$$ which can also be expressed as $$f(\mathbf{x})=(x_1-2)^2+4(x_2-1)^2-8.$$ I've deduced the minimizer $\mathbf{x^*}$ as $(2,1)$ with $f^*=-8$...
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### numerical optimization algorithm with approximate Gradient and Hessian only!

Suppose I have a energy functional E depending on X, where X is a N-dimensional real value vector and N could be very large (~=2000). I assume that there exists (at least) a (local) minimizer for E. ...
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### Understanding a bound in numerical optimization

I'm reading through the deepest descent method, and I'm struggling to understand a specific bound. I'll try to be as much clear as I can, but the notation used is a bit messy. It is basically ...
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