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Convex approximation of the non-convex function

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0

$begingroup$

I have the following constraint for the optimization problem in hand:

$$fracb_klog_2 left(1 + fracp_k alpha_ksum_j neq k p_j alpha_j + sum_n sum_l Xi_n,l,k 2^-2 v_n,l right) + 2 fracsum_n sum_l v_n,l C_F leq epsilon$$

where the variables are $v_n,l$, $p_k$, $p_j, ; j neq k$. The constants are $alpha_k$, $alpha_j$, $b_k$, $C_F$, $Xi_n,l,k$.

The constraint is non-convex in $v_n,l, p_k, p_j, ; j neq k$. I am looking solve the problem with sucessive convex approximation approach.

I need some suggestion on feasibilty of the problem in terms of it if its possible to have a convex approximation for the above constraint and or suggest some method to solve it.

optimization nonlinear-optimization non-convex-optimization

share|cite|improve this question

edited 1 hour ago

Javi

3,0212832

asked 16 hours ago

Chandan PradhanChandan Pradhan

353

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  The Optimization Ocean is full of hopelessness, with a few archipelagos of tiny atolls (e.g., LP, QP, SDP, etc) where life is easy.
  $endgroup$
  – Rodrigo de Azevedo
  15 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Any particular reason for manually deriving convex approximations and then using an iterative approach, instead of simply using a general purpose nonlinear solver which effectively does this for you, but with added general tricks and knowledge to handle nonlinear programs.
  $endgroup$
  – Johan Löfberg
  13 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @JohanLöfberg My idea was to solve the problem with respect to both $v_n,l$ and $p_k$ and formulate and SCA problem. I am not sure if it can be solved using non-linear solvers. I dont have experience with nonlinear solver and that's why I am not sure feasibility of the problem.
  $endgroup$
  – Chandan Pradhan
  12 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Nonlinear solvers solve, well, nonlinear problems. Your problem is nonlinear. Most often when people start messing abour with homemade sequential convex approximations etc, they are simply reinventing the wheel, or bad approximations of a very standard wheel. Start with a standard nonlinear solver and see where it gets you. If that isn't good enough, try developing your own heuristics.
  $endgroup$
  – Johan Löfberg
  6 hours ago
  

  
  
  
  

add a comment | 

0

$begingroup$

I have the following constraint for the optimization problem in hand:

$$fracb_klog_2 left(1 + fracp_k alpha_ksum_j neq k p_j alpha_j + sum_n sum_l Xi_n,l,k 2^-2 v_n,l right) + 2 fracsum_n sum_l v_n,l C_F leq epsilon$$

where the variables are $v_n,l$, $p_k$, $p_j, ; j neq k$. The constants are $alpha_k$, $alpha_j$, $b_k$, $C_F$, $Xi_n,l,k$.

The constraint is non-convex in $v_n,l, p_k, p_j, ; j neq k$. I am looking solve the problem with sucessive convex approximation approach.

I need some suggestion on feasibilty of the problem in terms of it if its possible to have a convex approximation for the above constraint and or suggest some method to solve it.

optimization nonlinear-optimization non-convex-optimization

share|cite|improve this question

edited 1 hour ago

Javi

3,0212832

asked 16 hours ago

Chandan PradhanChandan Pradhan

353

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  The Optimization Ocean is full of hopelessness, with a few archipelagos of tiny atolls (e.g., LP, QP, SDP, etc) where life is easy.
  $endgroup$
  – Rodrigo de Azevedo
  15 hours ago
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  Any particular reason for manually deriving convex approximations and then using an iterative approach, instead of simply using a general purpose nonlinear solver which effectively does this for you, but with added general tricks and knowledge to handle nonlinear programs.
  $endgroup$
  – Johan Löfberg
  13 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @JohanLöfberg My idea was to solve the problem with respect to both $v_n,l$ and $p_k$ and formulate and SCA problem. I am not sure if it can be solved using non-linear solvers. I dont have experience with nonlinear solver and that's why I am not sure feasibility of the problem.
  $endgroup$
  – Chandan Pradhan
  12 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Nonlinear solvers solve, well, nonlinear problems. Your problem is nonlinear. Most often when people start messing abour with homemade sequential convex approximations etc, they are simply reinventing the wheel, or bad approximations of a very standard wheel. Start with a standard nonlinear solver and see where it gets you. If that isn't good enough, try developing your own heuristics.
  $endgroup$
  – Johan Löfberg
  6 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

I have the following constraint for the optimization problem in hand:

$$fracb_klog_2 left(1 + fracp_k alpha_ksum_j neq k p_j alpha_j + sum_n sum_l Xi_n,l,k 2^-2 v_n,l right) + 2 fracsum_n sum_l v_n,l C_F leq epsilon$$

where the variables are $v_n,l$, $p_k$, $p_j, ; j neq k$. The constants are $alpha_k$, $alpha_j$, $b_k$, $C_F$, $Xi_n,l,k$.

The constraint is non-convex in $v_n,l, p_k, p_j, ; j neq k$. I am looking solve the problem with sucessive convex approximation approach.

I need some suggestion on feasibilty of the problem in terms of it if its possible to have a convex approximation for the above constraint and or suggest some method to solve it.

optimization nonlinear-optimization non-convex-optimization

share|cite|improve this question

edited 1 hour ago

Javi

3,0212832

asked 16 hours ago

Chandan PradhanChandan Pradhan

353

$endgroup$

share|cite|improve this question

edited 1 hour ago

Javi

3,0212832

asked 16 hours ago

Chandan PradhanChandan Pradhan

353

share|cite|improve this question

edited 1 hour ago

Javi

3,0212832

asked 16 hours ago

Chandan PradhanChandan Pradhan

353

edited 1 hour ago

Javi

3,0212832

edited 1 hour ago

Javi

3,0212832

asked 16 hours ago

Chandan PradhanChandan Pradhan

353

asked 16 hours ago

Chandan PradhanChandan Pradhan

353