Calculation of solution space for a linear matrix inequalities.

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A linear matrix inequality is given such that:



$A(x)<=0$ (Negative Semidefinite)



Where,
$A(x)=A_o+A_1*x_1+A_2*x_2....=A_o+sum_iA_ix_i$



If $A(x), A_i in mathbbR^ntimes n$, then how can I construct the entire space (in $x$) where the LMI holds?




linear-algebra matrices




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  • 1




    "Construct" in what sense?
    – Michal Adamaszek
    Aug 23 at 8:16










  • Obtaining the range of each element of $x$ within which the LMI holds.
    – Parikshit Pareek
    Aug 23 at 8:22






  • 1




    The LMI defines a nonlinear constraint, so it is hard to say that it holds for each element of $x$ in some range. It defines some more complicated convex set. What do you want to do with that set?
    – Michal Adamaszek
    Aug 23 at 8:52










  • I want to construct an inner approximation of that convex set where this inequality holds i.e. an element-wise range where the LMI is satisfied for sure.
    – Parikshit Pareek
    Aug 23 at 8:57














up vote
0
down vote

favorite












A linear matrix inequality is given such that:



$A(x)<=0$ (Negative Semidefinite)



Where,
$A(x)=A_o+A_1*x_1+A_2*x_2....=A_o+sum_iA_ix_i$



If $A(x), A_i in mathbbR^ntimes n$, then how can I construct the entire space (in $x$) where the LMI holds?




linear-algebra matrices




share|cite|improve this question
















  • 1




    "Construct" in what sense?
    – Michal Adamaszek
    Aug 23 at 8:16










  • Obtaining the range of each element of $x$ within which the LMI holds.
    – Parikshit Pareek
    Aug 23 at 8:22






  • 1




    The LMI defines a nonlinear constraint, so it is hard to say that it holds for each element of $x$ in some range. It defines some more complicated convex set. What do you want to do with that set?
    – Michal Adamaszek
    Aug 23 at 8:52










  • I want to construct an inner approximation of that convex set where this inequality holds i.e. an element-wise range where the LMI is satisfied for sure.
    – Parikshit Pareek
    Aug 23 at 8:57












up vote
0
down vote

favorite









up vote
0
down vote

favorite











A linear matrix inequality is given such that:



$A(x)<=0$ (Negative Semidefinite)



Where,
$A(x)=A_o+A_1*x_1+A_2*x_2....=A_o+sum_iA_ix_i$



If $A(x), A_i in mathbbR^ntimes n$, then how can I construct the entire space (in $x$) where the LMI holds?




linear-algebra matrices




share|cite|improve this question












A linear matrix inequality is given such that:



$A(x)<=0$ (Negative Semidefinite)



Where,
$A(x)=A_o+A_1*x_1+A_2*x_2....=A_o+sum_iA_ix_i$



If $A(x), A_i in mathbbR^ntimes n$, then how can I construct the entire space (in $x$) where the LMI holds?





linear-algebra matrices





share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 23 at 8:14









Parikshit Pareek

356




356







  • 1




    "Construct" in what sense?
    – Michal Adamaszek
    Aug 23 at 8:16










  • Obtaining the range of each element of $x$ within which the LMI holds.
    – Parikshit Pareek
    Aug 23 at 8:22






  • 1




    The LMI defines a nonlinear constraint, so it is hard to say that it holds for each element of $x$ in some range. It defines some more complicated convex set. What do you want to do with that set?
    – Michal Adamaszek
    Aug 23 at 8:52










  • I want to construct an inner approximation of that convex set where this inequality holds i.e. an element-wise range where the LMI is satisfied for sure.
    – Parikshit Pareek
    Aug 23 at 8:57












  • 1




    "Construct" in what sense?
    – Michal Adamaszek
    Aug 23 at 8:16










  • Obtaining the range of each element of $x$ within which the LMI holds.
    – Parikshit Pareek
    Aug 23 at 8:22






  • 1




    The LMI defines a nonlinear constraint, so it is hard to say that it holds for each element of $x$ in some range. It defines some more complicated convex set. What do you want to do with that set?
    – Michal Adamaszek
    Aug 23 at 8:52










  • I want to construct an inner approximation of that convex set where this inequality holds i.e. an element-wise range where the LMI is satisfied for sure.
    – Parikshit Pareek
    Aug 23 at 8:57







1




1




"Construct" in what sense?
– Michal Adamaszek
Aug 23 at 8:16




"Construct" in what sense?
– Michal Adamaszek
Aug 23 at 8:16












Obtaining the range of each element of $x$ within which the LMI holds.
– Parikshit Pareek
Aug 23 at 8:22




Obtaining the range of each element of $x$ within which the LMI holds.
– Parikshit Pareek
Aug 23 at 8:22




1




1




The LMI defines a nonlinear constraint, so it is hard to say that it holds for each element of $x$ in some range. It defines some more complicated convex set. What do you want to do with that set?
– Michal Adamaszek
Aug 23 at 8:52




The LMI defines a nonlinear constraint, so it is hard to say that it holds for each element of $x$ in some range. It defines some more complicated convex set. What do you want to do with that set?
– Michal Adamaszek
Aug 23 at 8:52












I want to construct an inner approximation of that convex set where this inequality holds i.e. an element-wise range where the LMI is satisfied for sure.
– Parikshit Pareek
Aug 23 at 8:57




I want to construct an inner approximation of that convex set where this inequality holds i.e. an element-wise range where the LMI is satisfied for sure.
– Parikshit Pareek
Aug 23 at 8:57















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