How do I optimize Ax = b such that every element of b is bigger than 0.5 and x has the lowest possible norm?












0












$begingroup$


As the title says I want to find x such that b, given by $Ax = b$
has ideally every element above 0.5
And x has the lowest possible norm.



A is a symmetric definite positive matrix



Thanks!!










share|cite|improve this question









$endgroup$












  • $begingroup$
    Maybe formulate as a linear problem and solve with simplex algorithm.
    $endgroup$
    – mathreadler
    Jan 1 at 18:08










  • $begingroup$
    what norm are we considering?
    $endgroup$
    – LinAlg
    Jan 1 at 18:36










  • $begingroup$
    @LinAlg the norm 2
    $endgroup$
    – Michael
    Jan 1 at 18:51










  • $begingroup$
    try YALMIP, should make formulating/solving easy
    $endgroup$
    – LinAlg
    Jan 1 at 18:54
















0












$begingroup$


As the title says I want to find x such that b, given by $Ax = b$
has ideally every element above 0.5
And x has the lowest possible norm.



A is a symmetric definite positive matrix



Thanks!!










share|cite|improve this question









$endgroup$












  • $begingroup$
    Maybe formulate as a linear problem and solve with simplex algorithm.
    $endgroup$
    – mathreadler
    Jan 1 at 18:08










  • $begingroup$
    what norm are we considering?
    $endgroup$
    – LinAlg
    Jan 1 at 18:36










  • $begingroup$
    @LinAlg the norm 2
    $endgroup$
    – Michael
    Jan 1 at 18:51










  • $begingroup$
    try YALMIP, should make formulating/solving easy
    $endgroup$
    – LinAlg
    Jan 1 at 18:54














0












0








0





$begingroup$


As the title says I want to find x such that b, given by $Ax = b$
has ideally every element above 0.5
And x has the lowest possible norm.



A is a symmetric definite positive matrix



Thanks!!










share|cite|improve this question









$endgroup$




As the title says I want to find x such that b, given by $Ax = b$
has ideally every element above 0.5
And x has the lowest possible norm.



A is a symmetric definite positive matrix



Thanks!!







matrices optimization matrix-equations






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 1 at 18:01









MichaelMichael

444




444












  • $begingroup$
    Maybe formulate as a linear problem and solve with simplex algorithm.
    $endgroup$
    – mathreadler
    Jan 1 at 18:08










  • $begingroup$
    what norm are we considering?
    $endgroup$
    – LinAlg
    Jan 1 at 18:36










  • $begingroup$
    @LinAlg the norm 2
    $endgroup$
    – Michael
    Jan 1 at 18:51










  • $begingroup$
    try YALMIP, should make formulating/solving easy
    $endgroup$
    – LinAlg
    Jan 1 at 18:54


















  • $begingroup$
    Maybe formulate as a linear problem and solve with simplex algorithm.
    $endgroup$
    – mathreadler
    Jan 1 at 18:08










  • $begingroup$
    what norm are we considering?
    $endgroup$
    – LinAlg
    Jan 1 at 18:36










  • $begingroup$
    @LinAlg the norm 2
    $endgroup$
    – Michael
    Jan 1 at 18:51










  • $begingroup$
    try YALMIP, should make formulating/solving easy
    $endgroup$
    – LinAlg
    Jan 1 at 18:54
















$begingroup$
Maybe formulate as a linear problem and solve with simplex algorithm.
$endgroup$
– mathreadler
Jan 1 at 18:08




$begingroup$
Maybe formulate as a linear problem and solve with simplex algorithm.
$endgroup$
– mathreadler
Jan 1 at 18:08












$begingroup$
what norm are we considering?
$endgroup$
– LinAlg
Jan 1 at 18:36




$begingroup$
what norm are we considering?
$endgroup$
– LinAlg
Jan 1 at 18:36












$begingroup$
@LinAlg the norm 2
$endgroup$
– Michael
Jan 1 at 18:51




$begingroup$
@LinAlg the norm 2
$endgroup$
– Michael
Jan 1 at 18:51












$begingroup$
try YALMIP, should make formulating/solving easy
$endgroup$
– LinAlg
Jan 1 at 18:54




$begingroup$
try YALMIP, should make formulating/solving easy
$endgroup$
– LinAlg
Jan 1 at 18:54










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