# Tagged Questions

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.

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### CVX problem formulation

Hello, I have a trouble formulating the statement for cvx Matlab package. Here x is a state variable, alpha, c1,c2 - contstants. Ai, Bi, di are matrices depending on Ai-1, Bi-1, di-1. One of the ...
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I have seen that cvx can deal with problems where the logarithm of something is maximized. In the binary file it says that cvx ...
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### From deterministic to stochastic LP formulations

I am having a hard time understanding the very first example in "A Tutorial on Stochastic Programming". More specifically the authors show that one can formulate the stochastic variant of (1.2) ...
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### Repeated 1d minimization with similar parameters (scipy)

I have a function f(x,k1,k2) and I am trying to minimize it over x for different values of ...
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### On Boyd et al.'s convergence analysis of ADMM: Why do we need the convexity assumption?

Please refer to Boyd et al.'s convergence analysis of ADMM (Chapter 3 and Appendix A). My question is: Why do we need $f$ and $g$ to be convex? I don't see the need of this assumption. If the ...
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In these notes (section 2.3), it is stated that: A point $x^*$ is a minimizer of a function $f$ (not necessarily convex) if and only if $f$ is subdifferentiable at $x^*$ and $0 \in\partial f(x^*).$...
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### How to solve a model with a quadratic term in the objective function on CPLEX?

I introduced a model with a quadratic objective function in CPLEX but it takes a long time to solve it, I think there is a way to tell CPLEX that the model has a quadratic objective function, but I ...
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### What is the fastest method for solving a quadratic programm repeatedly,( warmstarted)?

I would like to solve the following optimization problem \begin{align} \min_{x\in [0,1]^n} x^T p+ \frac{1}{2\lambda} x^T Q x \end{align} $Q$ is a positive semidefinite matrix. $\lambda>0$ is a ...
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### What method do you suggest to solve this minimax, quadratic in both variables problem?

I have a problem of the form, \begin{align} minimize_{y} maximize_{x}&\quad x^T y - y^T (B\odot x x^T) y\\ s.t. &x\in [l,u]\\ &Ay=b \end{align} How to efficiently solve this problem? ...
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### How to understand what's going wrong in a code for solving a problem with augmented lagrangian?

I am very new to optimization. so, sorry If I ask a simple question. I have a problem with a dozen of variables. I want to use Augmented Lagrangian for solving the problem. I write a code based on the ...
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### How to solve a constrained optimization problem using minFunc or minConf

I am trying to solve the following optimization problem: \begin{align} &\min\limits_{s} \rm{tr}\left(S^T S\right) + \mathrm{tr}\left(\left(S^T S\right)^{-2}\right)\\ &\text{subject to }\rm\...
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### Express the $\gamma_{2}^{\epsilon}$ SemiDefinite program in a form that is acceptable by SDPT3

I'm trying to express the following semidefinite program: for given $A \in R^{m \times n}$ and a scalar $\epsilon \in (0,1)$, \begin{align} &\gamma_{2}^{\epsilon}(A):= \min\,t\\ &\text{...
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### Implementation in R of $l_2$ penalized weighted quantile regression

I am struggling with such a minimization problem: $$min_{\mathbf{w}}~~\left( \lambda ||\mathbf{w}||^2 + \sum_{i=1}^{n}v_i |a_i - \mathbf{x_i}^\top\mathbf{w} - b | \right)$$ Here $v_i$ is weight of ...
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### Understanding the conditions for which ADMM can be applied

While reading Boyd's paper on ADMM I encountered an issue. Consider the following problem: Problem. Minimize $f(u) + g(v)$ subject to $Au + Bv = c$, where $f$ and $g$ are closed, proper, convex and ...
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### Difference of convex functions optimization problem in R

I am seeking of any already written R package which could help in optimization technique which is called Difference of convex functions. This technique is sketched here and could be very useful for ...
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### How to efficently solve: min $\sum_{ij}(a_{ij}x_{ij}^2 + b_{ij}x_{ij})$ s.t

I am trying to solve the following problem, where $a_{ij} \ge 0 \ \forall i,j$: \begin{align} \mbox{minimize}\quad & \sum_{i=1}^m\sum_{j=1}^n (a_{ij}x_{ij}^2 + b_{ij}x_{ij})\\ \mbox{subject to}\...
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### Storage complexity of SDP solver SCS

This is a follow up question to this question. Consider the following SDP in standard form: \begin{align} &\min_{X\in S^n, X>0} \operatorname{tr}(AX)\\ &\mbox{subject to}\; \operatorname{...
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### Best platform for complex SDPs with n and m around 5-15K?

I am looking to solve a class of SDPs with complex entries, with the semi-definite cone $S^n$, $n$ around 5000 to 15000. Also, $m$, the number of equality/inequality constraints is close to $n$. I ...
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### Maximizing a function over a polytope

I have to maximize $$f(x,y)=-\log(xy)$$ However I need it over the polytope $T=\mathrm{conv}\{(1/2,1/2),(1,2),(2,1)\}$ and this gives me problems: Then I get $$f_x(x,y)=1/x=0$$ $$f_y(x,y)=1/y=0$$ ...
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