# Tagged Questions

Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes

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### Can the extragradient method be computed only based on proximal steps?

As we know, for solving saddle point problems, the forward-backward algorithm is generally not guaranteed to converge. But the extragradient method converges Structured Prediction via the ...
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### A possible condition on a set of vectors to be uniquely determined by their gramian?

Suppose you are given a gramian matrix $G=W^TW\in R^{k\times k}$, $W\in R^{d\times k},\;d>k$. The given gramian $G$ determines, up to a unitary transformation, the columns of $W$, i.e. an ...
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### Dennis More' Superlinear Convergence_refrences request

Why in the proof of superlinear convergence of restricted broyden class (for the unconstrained optimization) we need the bounded deterioration condition for the approximation of all the true hessian ...
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### Which algorithm is most efficient for a specific QP problem

I have a QP problem of the following kind: $\min_{\alpha\in\mathbb{R}^n}\frac{1}{2}\alpha^T M \alpha - p^T\alpha$ s.t. $l\leq \alpha \leq u$ The matrix $M$ is symmetric and positive definite and of ...
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### Concavity of maxima [closed]

Suppose we have the following optimization problem : $\min\limits_x kf(x) + g(x)$ where $f$ is a decreasing convex function in $x$ and $g$ is an increasing convex function. Can we say that $x^*$ is ...
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### Designing Character Other Than Temperature for Simulated Annealing on Combinatorial Optimization

Many research on designing temperature for simulated annealing is carried out. We wonder if there is any research on designing general feature of the Hamiltonian used in Simulated Annealing. For ...
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### About optimization with Renyi divergence

Can someone link me to some pedagogic example of computing the Renyi divergence between two discrete/continuous distributions? Like examples where someone has been able to obtain a neat closed form or ...
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### Closed-form solution of a linear programming question

Among all the probability matrices \begin{equation*} P = \left(\begin{array}{cccc} p_{00} & p_{01} & \ldots & p_{0,J-1} \\ p_{10} & p_{11} & \ldots & p_{1,J-1} \\ \vdots & \...
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### Minimum of sum of modulus [closed]

How can I evaluate the minimum of $$\left|7x-1\right|+\left|7y-5\right|+\left|7z-1\right|$$ if $x,y,z$ are non negative reals such that $x+y+z=1$ and $y^2 \le xz$? Is there a standard way to ...
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### Global minimum of nonlinear least square

We have a continuous and differentiable function $f(\cdot)$ that maps from $R^n$ to $R^n$. We are trying to solve a nonlinear least square problem: Minimize $J(x)=\Vert f(x)-z\Vert^2$ subject to box ...
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### On optimizing a function whose projection and projected vector go through a linear transformation

Assume the two sets of vectors $\{\mathbf{a}_1,\ldots,\mathbf{a}_N\}$ and $\{\mathbf{b}_1,\ldots,\mathbf{b}_N\}$ of equal length. My goal is to find the optimum matrix $\mathbf{C}$ to the following ...
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### Question on solving an optimization problem using Variable splitting and ADMM

Tell me if I have found the right approach to the following optimization problem: $$min_{x} \frac{1}{2}\left \| Ax-b \right \|_2^2 \\ s.t. \ \ \Phi v=x \ , \ {x^T(1-x)}=0$$ $A$ and $\Phi$ ...
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### Envelope theorem for second derivative

I am maximizing a function $f(x,z)$ on $x$ ($z$ is treated a parameter in the maximization). The function $f$ is strictly concave on both variables. I know how to use the envelope theorem for the ...
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### Minimize sum of $\ell_2$ norm and linear combination, on simplex

Let $\Delta_n := \{x \in \mathbb{R}^n | x \ge 0, \sum_{1 \le i \le n}x_i = 1\}$ be the $n$-simplex. For $a, b \in \mathbb R^n$, with $\Delta_n \not \ni a$, consider the problem of computing the ...
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### Convex Optimization in an Ellipsoid

Suppose we want to minimize a linear objective inside an ellipsoid that is, $\min _x l^Tx$ such that $(x - \mu)^TA(x - \mu) \leq \beta ^2$. Here, A is PSD and $\mu$ is a fixed vector. Can this be ...
Let $H$ be a finite semigroup containing $n$ elements from a compact group $G$. I am trying to solve $$\max_{h_i,\ h_j\ \in\ H} \operatorname{tr} \sum_{i,\ j\ \leq\ n} \rho(h_i^{-1} h_j)(A_j A_i^T)$$...