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Quadratic Optimization problem with sqrt term
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I am trying to solve a mean-variance (quadratic optimization) problem with a non-linear market impact cost term in there. This is the problem I am trying to solve
$$max alpha a - gamma x^T Sigma x - asqrt $$
where, $x_0$ is the current portfolio holding.
I am using MATLAB's quadprog program to solve this problem. How can I setup my optimization problem correctly to incorporate the sqrt term in the objective ? I am sure there is a way to do this, but I am not aware of it.
optimization convex-optimization
edited Jul 30 at 15:23
LinAlg
5,4111319
asked Jul 30 at 15:22
silencer
1134
add a comment |Â
up vote
0
down vote
favorite
I am trying to solve a mean-variance (quadratic optimization) problem with a non-linear market impact cost term in there. This is the problem I am trying to solve
$$max alpha a - gamma x^T Sigma x - asqrt $$
where, $x_0$ is the current portfolio holding.
I am using MATLAB's quadprog program to solve this problem. How can I setup my optimization problem correctly to incorporate the sqrt term in the objective ? I am sure there is a way to do this, but I am not aware of it.
optimization convex-optimization
edited Jul 30 at 15:23
LinAlg
5,4111319
asked Jul 30 at 15:22
silencer
1134
2
Your problem is not convex due to the square root, therefore quadprog cannot optimize it. Why not use a norm?
– LinAlg
Jul 30 at 15:24
2
I thought market impacts were more commonly 3/2 power terms?
– Michael Grant
Jul 30 at 20:43
2
Regardless—quadprog will not be able to handle this. As its name implies, it supports only quadratic objectives; and if memory serves, only linear constraints. There is no way to render this objective, or even the $3/2$ version, under those limitations.
– Michael Grant
Jul 31 at 14:05
What are the decision variables? Is $a$ a decision variable? Is it only $x$?
– Alex Shtof
Aug 1 at 6:14
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am trying to solve a mean-variance (quadratic optimization) problem with a non-linear market impact cost term in there. This is the problem I am trying to solve
$$max alpha a - gamma x^T Sigma x - asqrt $$
where, $x_0$ is the current portfolio holding.
I am using MATLAB's quadprog program to solve this problem. How can I setup my optimization problem correctly to incorporate the sqrt term in the objective ? I am sure there is a way to do this, but I am not aware of it.
optimization convex-optimization
edited Jul 30 at 15:23
LinAlg
5,4111319
asked Jul 30 at 15:22
silencer
1134
I am trying to solve a mean-variance (quadratic optimization) problem with a non-linear market impact cost term in there. This is the problem I am trying to solve
$$max alpha a - gamma x^T Sigma x - asqrt $$
where, $x_0$ is the current portfolio holding.
I am using MATLAB's quadprog program to solve this problem. How can I setup my optimization problem correctly to incorporate the sqrt term in the objective ? I am sure there is a way to do this, but I am not aware of it.
optimization convex-optimization
edited Jul 30 at 15:23
LinAlg
5,4111319
asked Jul 30 at 15:22
silencer
1134
edited Jul 30 at 15:23
LinAlg
5,4111319
edited Jul 30 at 15:23
LinAlg
5,4111319
edited Jul 30 at 15:23
LinAlg
5,4111319
5,4111319
asked Jul 30 at 15:22
silencer
1134
asked Jul 30 at 15:22
silencer
1134
asked Jul 30 at 15:22
silencer
1134
1134
2
Your problem is not convex due to the square root, therefore quadprog cannot optimize it. Why not use a norm?
– LinAlg
Jul 30 at 15:24
2
I thought market impacts were more commonly 3/2 power terms?
– Michael Grant
Jul 30 at 20:43
2
Regardless—quadprog will not be able to handle this. As its name implies, it supports only quadratic objectives; and if memory serves, only linear constraints. There is no way to render this objective, or even the $3/2$ version, under those limitations.
– Michael Grant
Jul 31 at 14:05
What are the decision variables? Is $a$ a decision variable? Is it only $x$?
– Alex Shtof
Aug 1 at 6:14
add a comment |Â
2
Your problem is not convex due to the square root, therefore quadprog cannot optimize it. Why not use a norm?
– LinAlg
Jul 30 at 15:24
2
I thought market impacts were more commonly 3/2 power terms?
– Michael Grant
Jul 30 at 20:43
2
Regardless—quadprog will not be able to handle this. As its name implies, it supports only quadratic objectives; and if memory serves, only linear constraints. There is no way to render this objective, or even the $3/2$ version, under those limitations.
– Michael Grant
Jul 31 at 14:05
What are the decision variables? Is $a$ a decision variable? Is it only $x$?
– Alex Shtof
Aug 1 at 6:14
2
2
Your problem is not convex due to the square root, therefore quadprog cannot optimize it. Why not use a norm?
– LinAlg
Jul 30 at 15:24
Your problem is not convex due to the square root, therefore quadprog cannot optimize it. Why not use a norm?
– LinAlg
Jul 30 at 15:24
2
2
I thought market impacts were more commonly 3/2 power terms?
– Michael Grant
Jul 30 at 20:43
I thought market impacts were more commonly 3/2 power terms?
– Michael Grant
Jul 30 at 20:43
2
2
Regardless—quadprog will not be able to handle this. As its name implies, it supports only quadratic objectives; and if memory serves, only linear constraints. There is no way to render this objective, or even the $3/2$ version, under those limitations.
– Michael Grant
Jul 31 at 14:05
Regardless—quadprog will not be able to handle this. As its name implies, it supports only quadratic objectives; and if memory serves, only linear constraints. There is no way to render this objective, or even the $3/2$ version, under those limitations.
– Michael Grant
Jul 31 at 14:05
What are the decision variables? Is $a$ a decision variable? Is it only $x$?
– Alex Shtof
Aug 1 at 6:14
What are the decision variables? Is $a$ a decision variable? Is it only $x$?
– Alex Shtof
Aug 1 at 6:14
add a comment |Â
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2
Your problem is not convex due to the square root, therefore quadprog cannot optimize it. Why not use a norm?
– LinAlg
Jul 30 at 15:24
2
I thought market impacts were more commonly 3/2 power terms?
– Michael Grant
Jul 30 at 20:43
2
Regardless—quadprog will not be able to handle this. As its name implies, it supports only quadratic objectives; and if memory serves, only linear constraints. There is no way to render this objective, or even the $3/2$ version, under those limitations.
– Michael Grant
Jul 31 at 14:05
What are the decision variables? Is $a$ a decision variable? Is it only $x$?
– Alex Shtof
Aug 1 at 6:14