Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [convex-optimization]

Convex Optimization is a special case of mathematical optimization where the feasible region is convex and the objective is to either minimize a convex function or maximize a concave function.

Convex Optimization is a special case of mathematical optimization where the feasible region is convex and the objective is to either minimize a convex function or maximize a concave function. Linear Programming is a special case. Convex Optimization problems as a class are easier to solve numerically than general mathematical optimization problems.

254 questions
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How to intellligently attempt to rule out convexity?

I want to minimize a complicated objective function, and I'm not sure if it is convex. Is there a nice algorithm that attempts to prove that it is not convex? Of course the algorithm could fail to prove this, in which case I would not know if it…
MLE
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Biconvex optimization problems

Consider minimization of a biconvex function over a biconvex set. Is the biconvex optimization problems polynomially solvable?
Star
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Minimizing 1D convex functions

I have a one dimensional convex function $$f : [a,b] \to \mathbb{R}$$ and want to find the minimum value $$\min_{a \le x \le b} f(x)$$ I know all derivatives of $f$, so the problem could easily be solved with any 1D minimization method even ignoring…
Geoffrey Irving
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How to minimize ratio of L1 and square root of L2 norms

Here is the function I want to minimize: $$\sum_i\frac{\rho_{\tau}(1-\alpha-\pmb x_i^{\top}\pmb\beta)}{\sqrt{1+\pmb\beta^{\top}\pmb\beta}}$$ where $\alpha\in\mathbb{R}$, $\pmb\beta\in\mathbb{R}^p$ are the parameters we want to optimize over and…
user189035
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Minimal point of a intersection of $n$ convex sets is always the minimal point of the intersection of two convex sets?

I have the intuition that the minimal point (in the sense of having the lowest value in one of the Euclidean space dimensions) of a intersection of $n$ convex sets is always the minimal point of the intersection of two convex sets in the family.…
Adrian TC
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How to prove that a function is convex?

I'm calculating the gradient of a function with a symbolic math library called theano. Then I'm using gradient descent to find the minimum of the function. I'd like to prove that the minimum is a global minimum. How can I prove that my function is…
siamii
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Confusion while proving logdet function to be concave

I was going through this lecture related to convex optimization. It was proved that logdet function is concave. However, I didn't get the derivation at a part I didn't get how the step marked in red in the given picture was derived. Which property…
user34790
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Second-order derivative condition for convexity

It is written in a book I'm reading that $$\nabla f(x) = \left( \frac{\partial f(x)}{\partial x_1}, \frac{\partial f(x)}{\partial x_2},...,\frac{\partial f(x)}{\partial x_n}\right)$$ and $$\nabla^2 f(x)_{ij} = \frac{\partial^2 f(x)}{\partial x_i…
Kevin
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minimize function with convex constraints

I need to solve the following problem: For a given p=(x0,y0,z0,w0) and arbitrary T. For example , let p=(0.8,0.1,0.06,0.04) and T=-1.2. I need to find a vector q=(x,y,z,w) with the minimum distance from p, under the given constraints. I need a…
Mr Y
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Confusion related to convexity of 0-1 loss function

I am a bit confused why the 0-1 loss function is not convex. What's wrong with it?
user34790
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Confusion related to interior point method for optimization

I have this little confusion related to interior point method. In this method we use the log barrier function to approximate the real barrier which is not differential Now when we find the optimal solution for this objective with log barrier…
user34790
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Disciplined convex programming expression of $x\sqrt{1-x}$

Anyone have an idea for a DCP (disciplined convex programming) representation of the concave function $x\sqrt{1-x}$, which is has domain $[0,1]$? The Taylor series about $x=0$ is $$x - \frac{x^2}{2} - \frac{x^3}{8} - \frac{x^4}{16} +…
Dan Berkenstock
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Optimize multivariable function with interdependent variables

I have a cost function with 2 parameters. The variables are dependent on each other. So, if I just take a partial derivative with respect to one variable the slope is in terms of the other variable and vice-versa. So, how can I compute the optimal…
austin
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Is there any implementation of Nesterov's paper: Gradient methods for minimizing composite functions

I worked on a method based on this paper, "Gradient methods for minimizing composite functions". But unfortunately, every time I code it doesn't work. Even I investigate inequalities of the paper numerically, but I couldn't figure out what's the…
user85361
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beta in Nesterov's first method for piece wise linear convex optimization problem

I am trying to implement Nesterov's first method to solve convex piece-wise linear optimization problem, from this website: https://blogs.princeton.edu/imabandit/2013/04/01/acceleratedgradientdescent/ But then, such $\beta$ does not exist convex…
user40780
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