1
vote
1answer
23 views

Quadratic Problen with 2 constraints

Could someone help me to solve the following: $\min x^Tx$ s.t. $x^T a=1$ $x^T b=0$ where $x$,$a$ and $b$ are $(N\times1)$ vectors and $1$ and $0$ scalars. Thank you!
0
votes
0answers
23 views

Determining initial values for optimization problem

I am trying to solve an optimization problem with a quadratic objective function and non-linear constraints, using SQP (Sequential Quadratic Programming). I am attempting at doing the implementation ...
0
votes
0answers
9 views

First and second derivatives of barrier term in a quadratic programming problem

I am implementing an algorithm of Dang and Xu's, ``Non-convex Quadratic Programming Problem with Box Constraints'' and I'm hoping that somebody could verify what I'm doing. Their algorithm minimizes ...
0
votes
0answers
22 views

How to check if steepest gradient method will converge?

So I have this function $ f(x,y) = x^4 - 2x^2 +x + 4y^2 $ and I want to know if the steepest gradient method will converge if I pick an arbitrary point and apply said method. My initial thought ...
1
vote
0answers
49 views

Linear Complementarity Problem - multiple solutions, which one will it find?

If I have a inequality constrained system: w = Mz + q <= 0, z<=0, z^T w = 0 that for some given properties M and ...
3
votes
1answer
218 views

Optimization problem with ratio objective

I need to solve the following optimization problem $$ \text{maximize} \quad \frac{(a^T x)^2}{x^TBx+c^T|x|} \quad \text{subject to} \quad \|x\|_1=1 \quad (\text{or alternatively} \quad c^T|x|=1), $$ ...
0
votes
1answer
149 views

Convex optimization problem to quadratic programming problem

Briefly, have the following problem: \begin{equation} \sum_{i = 0}^n a_i \ (max [ F_i( \bar x ), 0 ] )^2 \rightarrow min, \\\\ s.t.\\\\ A \bar x \leq b \end{equation} where $ F( \bar x ) $ is a ...
4
votes
2answers
378 views

Analog of Simplex Method for Quadratic Programming

It happened so I need to work with an algorithm for solving QP problems. The main issue here is that I can't find any references to this algorithms (at least no references in sources in english). ...