Questions tagged [convex-optimization]

Convex optimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. The convexity property can make optimization in some sense "easier" than the general case - for example, any local minimum must be a global minimum.

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Modeling $-\ln(1 - w \cdot \sigma(x))$ as disciplined convex programming

Given $0 < w \leq 1$, I would like to use the function: $$-\ln(1 - w \sigma(t)),$$ where $\sigma(t) = 1 / (1 + \exp(-t))$ is the sigmoid function, in my objective. It's a bit tedious, but this ...
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How is this function piece-wise linear?

I encountered this lemma in a research paper related to End-to-End inventory management model. Please note that $d_{[t_1,t_2]} = \sum_{t=t_1}^{t_2} d_i$, where $d_t$ denotes demand at time instance t. ...
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Time complexity of QP solver

Could you suggest any papers or other resources that report the computational time complexity (e.g., O(n^3)) of the OSQP solver for Quadratic Programming (convex optimization), or at least the ...
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Minimal example using MOSEK API in python

I want to solve (simplified version) \begin{equation*} \begin{aligned} & \underset{}{\text{find}} & & X\in\mathbb{S}^{n}_{+}, x \in \mathbb{R}^{m}, \nu \in \mathbb{R}, \lambda\...
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Inconsistent solutions to linear optimal control problem

Consider the following optimal control problem: \begin{align} J(t) = \inf_{u(t)} \ & \frac{1}{2} \int_0^\infty e^{-\delta t} \left( x(t)^2 + \lambda y(t)^2 \right) dt \\ s.t. \ &u(t) \geq - \...
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Understanding different norms in the p-Wasserstein distance

The generalized p-Wasserstein distance, for $p\geq 1$, is given by $$d_W(Q_1,Q_2):=inf \left\{\int_{\Xi_2}||\xi_1-\xi_2||^p \Pi(d\xi_1,d\xi_2)\right\}$$ where $\Pi$ is the joint distribution of $\xi_1$...
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How to model this constraint in a better way?

I have a resource allocation problem. There are $M$ users and $N$ resources (machines). One user can be assigned to multiple resources/machines. But maximum $B$ machines can be activated at a time for ...
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Is the linearization with first-order Taylor approximation correct?

I have a QP problem as $\min \hspace{2mm} x^TQx-c^Tx$ here $x$ in binary I want to transform it into a MILP by writing the objective function as $\min \hspace{2mm} z-c^Tx$ and then adding a constraint ...
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1 vote
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Why is there a separate area for PSD constraints and PSD variables in the Conic Benchmark Format?

This question pertains to the Conic Benchmark Format (CBF) for specifying a convex optimization problem. Here's a link to the specification. In the CBF specification, there are separate areas for ...
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Approximating a convex program

As I understand it, "approximating" a convex program usually refers to finding a solution that is approximately-feasible approximately-optimal. For example, in the book "Geometric ...
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Distributionally Robust Stochastic Programming - Help with derivation

I've been working through this book on robust optimization of electric energy systems, and in particular chapter 4 on distributionally robust optimization. In following the derivation of section 4.2.1....
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How to write this objective in CVXPY for quasiconvex programming?

I have the following objective that I want to maximize: \max_{U_T\in \mathbb{R}, x\in\mathbb{R}^T} J_\alpha(U_T) = \frac{\alpha}{\alpha-1}\log\left(\frac{\cosh(U_T)}{\cosh(\alpha U_T)^...
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I need help with finding a library or tutorial to parallel optimize given a black box function, assuming it's convex

I have a black box function to optimize with respect to 1-D input,$\beta$, and I also have other inputs, which I don't need to optimize, say (x,y). So, I need to optimize f($\beta$, x,y) over $\beta$. ...
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log-log regression as reward function in optimization problem

Consider the model $\hat{y}_t = e^{\text{trend} + \text{seasonality}} \prod_k^K x_{k, t}^{b_k}$ where $K$ denotes different investment alternatives. You can think that trend and seasonality are ...
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Quadratic optimisation with $\ell_1$ constraints with CVXPY

Crossposted on Mathematics SE I seek to minimize a convex quadratic objective subject to linear and $\ell_1$-based equality constraints. When I turn to CVXPY, an error is raised indicating that it ...
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Relaxing non-affine equality constraints in convex optimization

Consider the convex function $f$. In section 4.2.1 in these lecture notes, the author writes: 4.2.1 Relaxing non-affine equality constraints For functions $g_i(x)$, $i \in \{1,\dots,d\}$ that are ...
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What is the use of solvers that return approximately-feasible solutions?

Common methods for solving convex programs return solutions that are only approximately-feasible solutions. Here is an example (from lecture notes by Nemirovski on interior-point methods for convex ...
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Finding a starting ellipsoid and a minimum volume to approximate a convex optimization problem

Suppose we have a convex optimizatiom program: \begin{align} \min &\quad f_0(x)\\ s.t. &\quad h_i(x) = 0 && i=1,\ldots, p\\ &\quad g_i(x) \leq 0 && i=1,\ldots, m\\ &\...
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Is it possible to make a posynomial concave using a change of variables?

Note: this question was already posted on Math.SE but received no answers, so I'm re-posting it here for better reach. Consider the following posynomial with respect to the variables $x_1,\dots,x_n$: ...
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Consider the problem \begin{aligned} \min_{x} \quad & f(x) + g(x), \\ \textrm{s.t.} \quad & x \in X \end{aligned} \tag{1} where \$X \subset \...