# Tagged Questions

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### multi-objective optimization

I am currently encounterring a optimization problem. The goal is optimize an objective function A and B at the same time. But the problem is that optmizing A will almost always tradoff with B, such ...
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### Finding optimal hyperplane

I have a set of vectors $\{V_i\}$ in $n$-dimensional space. There is a number corresponded to each vector $\alpha_i = f(V_i)$ ($\alpha_i$ can be negative). I want to find a hyperplane which would ...
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### Non-convex maxmin optimization

I am dealing with the following maxmin optimization problem: $c^*, x^* = \arg\max\limits_{c \in C, x \in X} [f(c, x) + \min\limits_{\tilde{x} \in X} g(c, \tilde{x})]$ $f$ and $g$ are differentiable ...
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### How to characterise this non-linear optimisation (linear objective function, non-linear constraints)

I was wondering if someone may be able to help me characterise this optimisation problem as I am struggling to find a numerical library that will solve it and I suspect it is because I am using the ...
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### Monotonic transformation in numerical optimization

Taking the logarithm of the Cobb-Douglass utility function ($u = x_1^a * x_2^b$) yields a utility function whose argmin is somewhat easier to derive. Since the logarithm is monotonic for $u>0$, we ...
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### Optimization problem with a minimization sub-problem as a constraint

I have a problem, for predefined $x_0,z\in\mathbb{R}$, which looks like $$\min_{\alpha,x} \sum_{i=1}^n \alpha_i f_i(x_i,z)$$ subject to \begin{align} \sum_{i=1}^n \alpha_i &= 1 \\ \sum_{i=1}^n ...
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### Optimization - show that linearized feasible set is empty.

I need help in the following problem: Consider the following optimization problem $$\min_{x_1,x_2}-x_1-x_2\quad\text{s.t.}\quad x_1^2+x_ 2^2-1=0,\quad x_1,x_2\geqslant 0.$$ Show that the ...
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### Initialization of Limited-memory BFGS (using libLBFGS)

I am using the package libLBFGS in order to minimize an objective function, for which the first derivative (with respect to the optimization variable) is known and computable. I use the default ...
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### Multi objective optimization into single objective.

I read that it is possible to convert a multi-objective optimization problem into single objective by using weighted sum method. I wanted to know if it is a good idea to convert a two objective ...
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### Allocation optimization problem

Imagine that I have $1$ million dollars which I want to invest. I have a set of $N$ elements in which I can put the money and obtain a revenue. Each element has a function that determines how much ...
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### Circle Packing: Unsolved Problem in Geometry?

Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for ...
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Is there any example of a continuous differentiable function out there, in which the gradient method with Armijo's stepsize-rule doesn't converge? I found it pretty hard to create one myself because ...
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### surface approximation using least squares

I am studying the following problem. Soppose you have two BeziÃ¨r patches with a common curve; suppose that the control points of the two patches are given by some initial guess (they are all known). ...
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### Does convexity of a function guarantee tractability of finding its minimum?

Formulating a problem as a convex optimization problem usually implicitly considered to imply being able to find global minimizer of the objective. My question is that if it is true or not. ...