Upper bound on distance between minimizers of two convex objective functions

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Assume we have two convex objective functions, $f$ and $tildef$, where

$$ f(x) leq tildef(x), quad forall x in mathbbR^d$$

Let

$$beginaligned x^* &:= argmin_x f(x)\ tildex^* &:= argmin_x tildef(x)endaligned$$

How to obtain an upper bound for $| x^*-tildex^* |$?

I think that this problem is way too general. But is there any paper, or method which suggest a method for a problem of this type?

optimization convex-optimization

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edited Jul 28 at 7:40

Rodrigo de Azevedo

12.6k41751

asked Jul 23 at 15:37

user85361

331215

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Such an upper bound does not exist in general. Are you asking for additional conditions that potentially do ensure such a result exists?
  – Marc
  Jul 23 at 16:10
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Marc, Yes. and if there is an example that one found this upper bound for a problem.
  – user85361
  Jul 24 at 0:12
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @RodrigodeAzevedo, what do you mean by quantifiers?
  – user85361
  Jul 28 at 7:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @RodrigodeAzevedo, yes. Thank you.
  – user85361
  Jul 28 at 7:37
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

1

Assume we have two convex objective functions, $f$ and $tildef$, where

$$ f(x) leq tildef(x), quad forall x in mathbbR^d$$

Let

$$beginaligned x^* &:= argmin_x f(x)\ tildex^* &:= argmin_x tildef(x)endaligned$$

How to obtain an upper bound for $| x^*-tildex^* |$?

I think that this problem is way too general. But is there any paper, or method which suggest a method for a problem of this type?

optimization convex-optimization

share|cite|improve this question

edited Jul 28 at 7:40

Rodrigo de Azevedo

12.6k41751

asked Jul 23 at 15:37

user85361

331215

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Such an upper bound does not exist in general. Are you asking for additional conditions that potentially do ensure such a result exists?
  – Marc
  Jul 23 at 16:10
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Marc, Yes. and if there is an example that one found this upper bound for a problem.
  – user85361
  Jul 24 at 0:12
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @RodrigodeAzevedo, what do you mean by quantifiers?
  – user85361
  Jul 28 at 7:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @RodrigodeAzevedo, yes. Thank you.
  – user85361
  Jul 28 at 7:37
  

  
  
  
  

add a comment | 

up vote
0
down vote

favorite

1

up vote
0
down vote

favorite

1

1

Assume we have two convex objective functions, $f$ and $tildef$, where

$$ f(x) leq tildef(x), quad forall x in mathbbR^d$$

Let

$$beginaligned x^* &:= argmin_x f(x)\ tildex^* &:= argmin_x tildef(x)endaligned$$

How to obtain an upper bound for $| x^*-tildex^* |$?

I think that this problem is way too general. But is there any paper, or method which suggest a method for a problem of this type?

optimization convex-optimization

share|cite|improve this question

edited Jul 28 at 7:40

Rodrigo de Azevedo

12.6k41751

asked Jul 23 at 15:37

user85361

331215

Assume we have two convex objective functions, $f$ and $tildef$, where

$$ f(x) leq tildef(x), quad forall x in mathbbR^d$$

Let

$$beginaligned x^* &:= argmin_x f(x)\ tildex^* &:= argmin_x tildef(x)endaligned$$

How to obtain an upper bound for $| x^*-tildex^* |$?

I think that this problem is way too general. But is there any paper, or method which suggest a method for a problem of this type?

optimization convex-optimization

share|cite|improve this question

edited Jul 28 at 7:40

Rodrigo de Azevedo

12.6k41751

asked Jul 23 at 15:37

user85361

331215

share|cite|improve this question

share|cite|improve this question

edited Jul 28 at 7:40

Rodrigo de Azevedo

12.6k41751

edited Jul 28 at 7:40

Rodrigo de Azevedo

12.6k41751

edited Jul 28 at 7:40

Rodrigo de Azevedo

12.6k41751

12.6k41751

asked Jul 23 at 15:37

user85361

331215

asked Jul 23 at 15:37

user85361

331215

asked Jul 23 at 15:37

user85361

331215

331215

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Such an upper bound does not exist in general. Are you asking for additional conditions that potentially do ensure such a result exists?
  – Marc
  Jul 23 at 16:10
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Marc, Yes. and if there is an example that one found this upper bound for a problem.
  – user85361
  Jul 24 at 0:12
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @RodrigodeAzevedo, what do you mean by quantifiers?
  – user85361
  Jul 28 at 7:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @RodrigodeAzevedo, yes. Thank you.
  – user85361
  Jul 28 at 7:37
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Such an upper bound does not exist in general. Are you asking for additional conditions that potentially do ensure such a result exists?
  – Marc
  Jul 23 at 16:10
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @Marc, Yes. and if there is an example that one found this upper bound for a problem.
  – user85361
  Jul 24 at 0:12
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @RodrigodeAzevedo, what do you mean by quantifiers?
  – user85361
  Jul 28 at 7:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @RodrigodeAzevedo, yes. Thank you.
  – user85361
  Jul 28 at 7:37
  

  
  
  
  

1

1

Such an upper bound does not exist in general. Are you asking for additional conditions that potentially do ensure such a result exists?
– Marc
Jul 23 at 16:10

Such an upper bound does not exist in general. Are you asking for additional conditions that potentially do ensure such a result exists?
– Marc
Jul 23 at 16:10

@Marc, Yes. and if there is an example that one found this upper bound for a problem.
– user85361
Jul 24 at 0:12

@Marc, Yes. and if there is an example that one found this upper bound for a problem.
– user85361
Jul 24 at 0:12

@RodrigodeAzevedo, what do you mean by quantifiers?
– user85361
Jul 28 at 7:30

@RodrigodeAzevedo, what do you mean by quantifiers?
– user85361
Jul 28 at 7:30

@RodrigodeAzevedo, yes. Thank you.
– user85361
Jul 28 at 7:37

@RodrigodeAzevedo, yes. Thank you.
– user85361
Jul 28 at 7:37

add a comment | 

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