Complexity of a quadratic program

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Discussion Overview

The discussion revolves around the complexity of solving a quadratic program defined by a specific minimization problem with linear constraints. Participants are exploring the computational complexity and methods for solving this type of optimization problem.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks help in computing the complexity of a quadratic program involving a positive definite matrix Q and constraints defined by matrix A.
  • Another participant questions what is meant by the complexity of a quadratic program, indicating a need for clarification on the term.
  • A participant reiterates the inquiry about determining the computational complexity or time required to solve the problem.
  • Another participant mentions the Wolf algorithm, suggesting it reduces the quadratic program to a series of linear programs, though they express uncertainty about the overall complexity implications.

Areas of Agreement / Disagreement

There is no consensus on the definition of complexity in this context, and multiple views on how to approach the problem remain. Participants express varying levels of understanding and knowledge about the topic.

Contextual Notes

Participants have not defined key terms such as "complexity" or provided specific mathematical frameworks for analysis. The discussion lacks detailed exploration of the assumptions underlying the quadratic program and the implications of using the Wolf algorithm.

Socal93
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I'm trying to compute the complexity of the quadratic program: $$\displaystyle\min_{\mathbf{X}} (\mathbf{X^TQX +C^TX}) \quad{} \text{subject to} \quad{} \mathbf{A X \leq Y}$$
A is MxN and X is Nx1. Q is positive definite and I'm using the interior point method. Any help in computing the complexity would be appreciated.
 
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You have caught my curiosity. What is meant by the complexity of a quadratic program?
 
I'm trying to determine the computational complexity or the time it takes to solve the above problem.
 
Socal93 said:
I'm trying to determine the computational complexity or the time it takes to solve the above problem.

Don't know anything about that. I do know that the Wolf algorithm reduces the quadratic program to a finite sequence of linear programs.
 

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