# Tagged Questions

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### Convex, differentiable approximation of optimization objective function

I have defined an objective function $$f(E,B)=\sum_i \max\{ \text{abs}\{\epsilon_i\}-b_i,0 \}$$ for $\epsilon_i \in \text{E}$, deviations of a function from some target observations, and $b_i \in B$, ...
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### Optimization of Inputs to Monte Carlo Simulation Based on Outputs

I have an optimization process that seems to work, but I want to better understand why it works and whether there's a better way to do what I'm trying to achieve. Basically I am optimizing two (or ...
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### Separable linear programs

Assume, we have two distinct LPs: \begin{equation*} \begin{aligned} & \text{min}_{x_1} & & c_1^Tx_1 \\ & \text{subject to} & & A_1x_1 = b \\ & & & x_1 \geq 0 \\ ...
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### Convex optimization where both the region and function are ugly

I am trying to build a gradient descent algorithm for a convex function over a convex region in high dimension with no closed form. All I can do is: Check whether a point is in the region Evaluate ...
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### If weighted-sum scalarization is ok with concave function?

I want to ask a basic question related to optimization. I read that weighted-sum scalarization of multi-objective optimization problem cannot explore Pareto-front on a part of function where it is ...
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### Holding the constraints of a constrained optimization when transformed into unconstrained optimization

Suppose there is a constrained convex optimization problem as shown below \begin{aligned} & \min\limits_{\mathbf{x}} & & f(\mathbf{x}) \\ & \text{s.t.} & & ...
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### Projecting on the constraint set $X = UU^T$

I'd like to explore projecting $(\hat X, \hat U)$ on the nonconvex constraint set $\{(X,U) \mid X = UU^T, U \text{ has$r$columns}\}$ where $\hat X$ is a symmetric matrix and $\hat U$ is some ...