Mixing
min z under these constrains
0
$begingroup$
$$min_{x,z} { z : z geq x^TA_{i}x ; (i=1,ldots,k), ; x^Tx=1}$$
$x$ is a vector and $A_{i}, i=1,2,...k $ are given matrixes
linear-algebra optimization
edited Jan 7 at 1:47
LinAlg
9,0111521
asked Jan 6 at 18:37
VidaVida
12
$endgroup$
add a comment |
0
$begingroup$
$$min_{x,z} { z : z geq x^TA_{i}x ; (i=1,ldots,k), ; x^Tx=1}$$
$x$ is a vector and $A_{i}, i=1,2,...k $ are given matrixes
linear-algebra optimization
edited Jan 7 at 1:47
LinAlg
9,0111521
asked Jan 6 at 18:37
VidaVida
12
$endgroup$
$begingroup$
Thank you for considering this problem. I am curious about the reason about the hardness. THX
$endgroup$
– Vida
Jan 7 at 1:31
$begingroup$
$x^Tx=1$ is a nonconvex constraint, and very little information is given about $A_i$. The case $k=1$ is easy via the S-lemma. If $A_i$ are positive semidefinite you can write it as $max{x^Tx : x^TA_ixleq t}$ and solve it for different values of $t$ until the optimal objective value is $1$. CPLEX and Gurobi can now optimize nonconvex quadratic objectives over a convex quadratic domain.
$endgroup$
– LinAlg
Jan 7 at 1:50
$begingroup$
Thank you so much for the valuable information. I really need to reconsider the problem.
$endgroup$
– Vida
Jan 7 at 3:00
add a comment |
0
0
0
$begingroup$
$$min_{x,z} { z : z geq x^TA_{i}x ; (i=1,ldots,k), ; x^Tx=1}$$
$x$ is a vector and $A_{i}, i=1,2,...k $ are given matrixes
linear-algebra optimization
edited Jan 7 at 1:47
LinAlg
9,0111521
asked Jan 6 at 18:37
VidaVida
12
$endgroup$
$$min_{x,z} { z : z geq x^TA_{i}x ; (i=1,ldots,k), ; x^Tx=1}$$
$x$ is a vector and $A_{i}, i=1,2,...k $ are given matrixes
linear-algebra optimization
linear-algebra optimization
edited Jan 7 at 1:47
LinAlg
9,0111521
asked Jan 6 at 18:37
VidaVida
12
edited Jan 7 at 1:47
LinAlg
9,0111521
asked Jan 6 at 18:37
VidaVida
12
edited Jan 7 at 1:47
LinAlg
9,0111521
edited Jan 7 at 1:47
LinAlg
9,0111521
edited Jan 7 at 1:47
LinAlg
9,0111521
9,0111521
asked Jan 6 at 18:37
VidaVida
12
asked Jan 6 at 18:37
VidaVida
12
asked Jan 6 at 18:37
VidaVida
12
12
$begingroup$
Thank you for considering this problem. I am curious about the reason about the hardness. THX
$endgroup$
– Vida
Jan 7 at 1:31
$begingroup$
$x^Tx=1$ is a nonconvex constraint, and very little information is given about $A_i$. The case $k=1$ is easy via the S-lemma. If $A_i$ are positive semidefinite you can write it as $max{x^Tx : x^TA_ixleq t}$ and solve it for different values of $t$ until the optimal objective value is $1$. CPLEX and Gurobi can now optimize nonconvex quadratic objectives over a convex quadratic domain.
$endgroup$
– LinAlg
Jan 7 at 1:50
$begingroup$
Thank you so much for the valuable information. I really need to reconsider the problem.
$endgroup$
– Vida
Jan 7 at 3:00
add a comment |
$begingroup$
Thank you for considering this problem. I am curious about the reason about the hardness. THX
$endgroup$
– Vida
Jan 7 at 1:31
$begingroup$
$x^Tx=1$ is a nonconvex constraint, and very little information is given about $A_i$. The case $k=1$ is easy via the S-lemma. If $A_i$ are positive semidefinite you can write it as $max{x^Tx : x^TA_ixleq t}$ and solve it for different values of $t$ until the optimal objective value is $1$. CPLEX and Gurobi can now optimize nonconvex quadratic objectives over a convex quadratic domain.
$endgroup$
– LinAlg
Jan 7 at 1:50
$begingroup$
Thank you so much for the valuable information. I really need to reconsider the problem.
$endgroup$
– Vida
Jan 7 at 3:00
$begingroup$
Thank you for considering this problem. I am curious about the reason about the hardness. THX
$endgroup$
– Vida
Jan 7 at 1:31
$begingroup$
Thank you for considering this problem. I am curious about the reason about the hardness. THX
$endgroup$
– Vida
Jan 7 at 1:31
$begingroup$
$x^Tx=1$ is a nonconvex constraint, and very little information is given about $A_i$. The case $k=1$ is easy via the S-lemma. If $A_i$ are positive semidefinite you can write it as $max{x^Tx : x^TA_ixleq t}$ and solve it for different values of $t$ until the optimal objective value is $1$. CPLEX and Gurobi can now optimize nonconvex quadratic objectives over a convex quadratic domain.
$endgroup$
– LinAlg
Jan 7 at 1:50
$begingroup$
$x^Tx=1$ is a nonconvex constraint, and very little information is given about $A_i$. The case $k=1$ is easy via the S-lemma. If $A_i$ are positive semidefinite you can write it as $max{x^Tx : x^TA_ixleq t}$ and solve it for different values of $t$ until the optimal objective value is $1$. CPLEX and Gurobi can now optimize nonconvex quadratic objectives over a convex quadratic domain.
$endgroup$
– LinAlg
Jan 7 at 1:50
$begingroup$
Thank you so much for the valuable information. I really need to reconsider the problem.
$endgroup$
– Vida
Jan 7 at 3:00
$begingroup$
Thank you so much for the valuable information. I really need to reconsider the problem.
$endgroup$
– Vida
Jan 7 at 3:00
add a comment |
0
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$begingroup$
Thank you for considering this problem. I am curious about the reason about the hardness. THX
$endgroup$
– Vida
Jan 7 at 1:31
$begingroup$
$x^Tx=1$ is a nonconvex constraint, and very little information is given about $A_i$. The case $k=1$ is easy via the S-lemma. If $A_i$ are positive semidefinite you can write it as $max{x^Tx : x^TA_ixleq t}$ and solve it for different values of $t$ until the optimal objective value is $1$. CPLEX and Gurobi can now optimize nonconvex quadratic objectives over a convex quadratic domain.
$endgroup$
– LinAlg
Jan 7 at 1:50
$begingroup$
Thank you so much for the valuable information. I really need to reconsider the problem.
$endgroup$
– Vida
Jan 7 at 3:00