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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 ...
Robert Bassett's user avatar
1 vote
0 answers
202 views

MOSEK via fusion vs API vs CVXPY

In Python, I would like to solve a collection of problems, that are all solvable via MOSEK's conic optimization solvers (ExpCone, SOCP, etc.) I have tried CVXPY. I get very robust and reliable results,...
independentvariable's user avatar
5 votes
2 answers
474 views

Simple OLS problem can only be solved in SCS. Is the dual infeasible?

Essentially, I am trying to solve a simple orthogonal least-squares (OLS) problem with some constraints — the coefficients must sum to $1$, no coefficient can be less than $0$, and no coefficient can ...
Pipob Puthipiroj's user avatar
6 votes
1 answer
257 views

Is it possible to express these constraints with basic cones?

I have the following optimization problem: \begin{align}\min&\quad x\\ \text{s.t.}&\quad x=\max_{i} \{x_{i}\}\\ &\quad x_{i}y_{i}=z_{i}\\ &\quad x_{i}, y_{i}, z_{i}\geqslant0 \end{...
PNoug's user avatar
  • 61
5 votes
2 answers
1k views

Julia JuMP successive optimization

I am using Julia's JuMP package to solve a cutting-plane method. Namely, I solve a sub-problem, find the most-violated constraint in the master problem, add that to ...
independentvariable's user avatar
6 votes
1 answer
294 views

Compute Scaling factor(s) for linear constraint ($A@x<b$)

We optimize large-scale optimization problems with tens of thousands of variables and constraints with Cvxpy + Commercial solvers (e.g. Gurobi, Mosek). The coefficient range easily exceeds the ...
pqrz's user avatar
  • 470
12 votes
5 answers
2k views

Dividing machines into groups of equal sizes so that each group has approximately same productivity

I have set of machines with varying productivity. I want put the machines in different groups so that the groups have approximately equal productivity. Lets say, we have $M$ machines. and we want to ...
KGM's user avatar
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3 votes
1 answer
175 views

Mosek Fusion APIs

Does anyone know if there is a list of available function APIs for Mosek Fusion APIs? Namely, what functions are available, their arguments list and meaning, what they do. Something similar to UNIX ...
inf's user avatar
  • 129
3 votes
1 answer
244 views

Are short-sell allowed in conic formulation of Markowitz optimization?

Sorry to ask a question about the basic Markowitz portfolio optimization. The example is from Mosek's example book. The basic Markowitz portfolio optimization is formulated as: The book mentioned we ...
inf's user avatar
  • 129
1 vote
1 answer
180 views

Questions on Mosek Fusion Power Cone example

Just trying to understand the example given in Mosek Fusion handbook as shown I'm not exactly sure how to convert 7.3 to 7.4 in terms of objective function. I understand the power cone $P_{3}^{0.2, 0....
inf's user avatar
  • 129
6 votes
0 answers
138 views

Cases where RLT/SDP relaxation does not work well with standard quadratic optimization

(For people who don't know what RLT is): I am maximizing an indefinite quadratic function over a standard simplex, i.e., the standard quadratic optimization problem. A well-known approach is to relax ...
independentvariable's user avatar
5 votes
1 answer
221 views

Which solver solves PSD constrained convex non-linear problem

I have a problem with a vector variable $w \in \mathbb{R}^n$ and a symmetric matrix variable $V \in \mathbb{R^{n \times n}}$. I am solving a problem which is roughly like: \begin{align} \begin{array}{...
independentvariable's user avatar