# Questions tagged [numerical-optimization]

Numerical methods for continuous optimization.

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### Production time optimization model

I have a problem where I have 2 different types of raw-material. These materials can be processed in two different production-lines which take different amount of time, depending on raw material. ...
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### Hyperparameter optimization

How to choose hyper-parameters for optimisation methods in practice? I know that there are hyper-parameter optimisation techniques such as gradient-based or bayesian methods, but for instance it is ...
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### Numerical Integration Schemes for a Hemispherical Region

I am struggling with a problem that requires me to numerical integrate a function within a hemisphere. While the function is smooth, it is pretty nasty, extremely oscillatory and I have to calculate ...
1answer
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### Numerical integration in Finite Element Method (and implementation in Matlab)?

i'm trying to solve the p-Laplace Equation: \begin{align} \begin{cases} \text{div} (\sigma |\nabla u|^{p-2} \nabla u) = f &\quad \text{in } \Omega\\ u = g &\quad \text{in } \partial\Omega \...
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### Maximise $z = \frac{y}{2x+2y}+\frac{50-y}{200-2x-2y}$ given that $x+y$ is non zero and $x+y<100$. Also, $x\leq50$ and $y\leq50$ and non-negative.

Z is actually a probability function. I am finding where the probability is maximized. But I could find no way how to maximize this function. Original question is as follows: Mr A wants to join a ...
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### Optimal step size in gradient descent

Suppose a differentiable, convex function $F(x)$ exists. Then $b = a - \gamma\nabla F(a)$ implies that $F(b) \leq F(a)$ given $\gamma$ is chosen properly. The goal is to find the optimal $\gamma$ at ...
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### What are the directions of research in Numerical Optimization?

I have just begun reading in the field of Numerical Optimization. Are people trying to invent new Algorithms? or proving the convergence of Heuristic Algorithms? and what else? What are the tools a ...
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### Solving multiobjective problem with matlb

I would like to solve a multiobjective problem with matlab with NSGA II procedure. The problem is a maximization/minimizationf objective functions. Can someone porvide me this code, and explain how to ...
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### Encouraging sparse output in optimization problem

I am trying to define an optimization problem: $$\min_\theta \sum_{x\in X} L(x, \theta, f_\theta(x),\delta_\theta(x)) + \lambda_s S(\delta_\theta(x))$$ where $X$ is the dataset, $\theta$ are the ...
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### Global convergence of the BFGS method

Please help me prove that $$\det(B_{k+1})=\det(B_k)\frac{y_k^Ts_k}{s_k^TB_ks_k}$$ This is from the global convergence of the BFGS method (Quasi-Newton methods), where $B_k$ is the approximate ...
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### Rate of convergence of the steepest descent method on a general linear function

Can someone help me with the proof of this theorem (it's theorem 3.4 from the Nocedal and Wright book - Chapter 3 - Line search methods) regarding the convergence rate of the steepest descent method ...
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### Linear Programming, Optimal Solutions

I posted the whole question to give some context, but my problem lies with (iv). I think you're meant to use a formula for the generalization of the optimal solution, but I'm not really sure what this ...
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### Amortized Approximate Map Recovery

I want to implement Sparse Extended Information Filter Slam.I studied it from Probabilistic Robotics by Dr. Sebestian Thrun. I have some numerical doubt in chapter 12 page 321(Amortized Approximate ...
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### What is the difference between projected gradient descent and ordinary gradient descent?

I just read about projected gradient descent but I did not see the intuition to use Projected one instead of normal gradient descent. Would you tell me the reason and preferable situations of ...
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### If the relative value of the most negative eigenvalue is small, can we view the quadratic program as convex?

Consider symmetric matrix $A \in \mathbb{R}^{n \times n}$ with $n-1$ negative eigenvalues and a positive one such that $\lambda_1 > \lambda_2> \dots > \lambda_n$, where $\lambda_n$ is the ...
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### Quadratic Matrix programming

I would like to find a numerical solution to the following quadratic matrix programming problem. Square matrix A has thousands of rows, so I need a algorithm which works fast. I looked into Python but ...
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### The selection coordinates method of coordinates in the coordinate descent/ascent algorithm?

The selection coordinates method of coordinates in the coordinate descent/ascent algorithm? What I know: Cyclic select coordinates; Randomly select coordinates (with replace); Randomly select ...