This is for questions on Quadratic Programming (QP). A QP problem is the problem of minimising or maximising a quadratic objective function subject to affine constraints.

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5
votes
2answers
689 views

What numerical methods are known to solve $L_1$ regularized quadratic programming problems?

What numerical methods are suitable to solve the following problem $$\min_x \tfrac{1}{2}x^T A x + b^Tx + \lambda ||x||_1$$ where $x,b\in\mathbf{R}^n$, and $A\in \mathbf{R}^{n\times n}$ is positive ...
4
votes
0answers
79 views

Quadratic optimisation with quadratic equality constraints

I would like to solve the following optimisation problem: $\min_{x} (x'Ax)$ subject to $x'Bx = x'Cx = 1$. Where A is symmetric and B and C are diagonal. Does anyone have a suggestion for an ...
3
votes
1answer
426 views

Shortest Path and Minimum Curvature Path - implementation

Let's say we are given a race track, which may be described as a closed curve of given width (it may differ along the curve). My task is to implement an algorithm which finds two kinds of trajectories ...
3
votes
2answers
876 views

Quadratic Equality Constraints via SDP

I want to know if it is possible to solve a QCQP problem with quadratic equality constraints in SDP. I know it is possible to convert a QCQP to an SDP by using the Shur complement. The following ...
3
votes
1answer
179 views

binary quadratic optimization problem

I am trying to solve the following binary quadratic program. $$ \min_{\Delta} \Delta^T H \Delta + c^T\Delta \\ \text{Such that:} ~~~\Delta\in \{0,1\}^n ~~\text{and}~~ \sum_{i=1}^n \Delta_i \leq \Gamma ...
2
votes
0answers
165 views

Lagrange multiplier expression

I would like to solve the following optimization problem using the gradient ascend method: \begin{array}{ll} \text{maximize}_{\theta} & \theta^TQ_1\theta + b_1\\ \text{subject to} & \theta^...
1
vote
2answers
52 views

Given a set of vectors and a target vector, find the set of scaling factors that minimizes distance of sum of those vectors from target

I have a set of $n$ starting vectors $\vec i_n$ and a target vector $\vec t$. I have a set of scaling factors $a_n$ for which I can compute the sum $\vec s$: $$ \vec s = \sum_{i=1}^n {a_i \vec i_i} $$...
0
votes
1answer
163 views

Find a best 4-tuple which fulfils a variable boolean formula

I am looking for an algorithm... I have a kind of boolean formulae which contain $\wedge$, $\vee$, $+$ as arithmetic operator, relational operators ($<, >, \ldots)$, 4 integer constants $c_0, \...
0
votes
2answers
207 views

How to compute primal variable based on dual variables and their multipliers

I edited this question based on information I got from comments. Assume we have an optimization problem (primal problem). we solve it's dual using some kind of primal-dual interior point solver. So, ...