Dear experts,
I am new with CVX and cannot understand the point:
cvx_begin sdp
variable alpha(20,1)
minimize sum(alpha)+sum_square(alpha)
diag(alpha) >= B
cvx_end
This simple SDP model (I enclose matrix B below) shows Infeasible status when solved by SeDuMi under low precision and by SDPT3 under low and high precision (Inaccurate/Solved for SeDuMi under high precision).
When the objective function is changed to “minimize sum(alpha)” or the feasibility problem is considered, the status is Solved in all cases. Why does the objective function affect feasibility?
B is
-80,4761485955042 | -29,5748607748623 | 29,3372357331135 | 23,1204513942210 | -87,3323282888696 | -135,202388421630 | -397,174052587854 | -25,0118322817781 | -68,9220732243511 | -464,408261445729 | 354,436277014027 | -32,6210091306378 | 737,772968912729 | -40,7270370532508 | -43,7270434537630 | 4,27294747612693 | -36,7270631471949 | -34,7270819309761 | -28,2493957342700 | -47,2493989794566 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
-29,5748607748623 | -19,4612892475974 | 1210,13693658537 | 1316,95616088984 | 145,997218269826 | 4,44844994982859 | -424,869196192798 | 146,663066146686 | 70,1893695905364 | 417,227306683108 | 54,3930231232374 | 1226,29621493700 | 44,2756880428884 | 206,275685109065 | 1219,27568196156 | 2151,77567750125 | 102,775672277136 | 1153,27566304005 | 149,264690029108 | -23,2353115667414 |
29,3372357331135 | 1210,13693658537 | -94,4049585776183 | -84,8919616271516 | 375,458816712899 | 532,694409198063 | -869,027416764657 | 719,222853978773 | 292,020436378185 | 225,249046624667 | 313,090918595099 | 319,761956170420 | 266,348961468383 | 1272,34895500670 | 142,348948074382 | 396,348938250654 | 693,848926744659 | 536,348906400168 | 693,324738583861 | -51,1752649309627 |
23,1204513942210 | 1316,95616088984 | -84,8919616271516 | -76,3375701603701 | 392,055124234730 | 449,406143506336 | -743,195235945942 | 757,893322978464 | 269,134039310842 | 337,923277544196 | 187,650409777138 | 317,296997753149 | 238,503348281279 | 1269,50334247073 | 206,503336236965 | 802,003327403153 | 506,003317056595 | 638,503298762177 | 638,981566287893 | -46,0184368727489 |
-87,3323282888696 | 145,997218269826 | 375,458816712899 | 392,055124234730 | -152,639076401054 | -4,18885894175847 | -835,315247888661 | 617,425105832689 | 314,307955443979 | 4422,71615234540 | 51,6602195330760 | 712,108618884869 | 220,458594503794 | -33,5414137125955 | -32,5414225274268 | 477,958564981153 | 232,458550350638 | 93,9585244814797 | 334,927793751752 | -65,0722107175426 |
-135,202388421630 | 4,44844994982859 | 532,694409198063 | 449,406143506336 | -4,18885894175847 | -309,036202004281 | -958,078724065159 | 780,979573823801 | 7,84300331362681 | 7070,19909629300 | -61,8702234704563 | 636,731055964564 | 234,453130765985 | -56,5468809250466 | -62,5468934675959 | 427,953088758467 | 143,953067940830 | 1,45303113182250 | 239,409304634772 | -92,5907017245495 |
-397,174052587854 | -424,869196192798 | -869,027416764657 | -743,195235945942 | -835,315247888661 | -958,078724065159 | -12355,9105214192 | -1196,73493200854 | -911,917618688801 | -9045,98150781726 | -548,996631399145 | -741,232522450841 | 702,313322917668 | -565,186751006344 | -560,686830314621 | -461,186942701689 | -550,687074334490 | -529,687307082946 | 14007,0362042176 | -585,463835993231 |
-25,0118322817781 | 146,663066146686 | 719,222853978773 | 757,893322978464 | 617,425105832689 | 780,979573823801 | -1196,73493200854 | -154,516449356202 | -31,8584266433906 | 770,126739966631 | -1,54352369648362 | 276,986996571434 | 249,059830935245 | 42,5598226684816 | 45,5598137996073 | 423,559801231603 | 108,559786511389 | 93,5597604836297 | 828,028841346297 | 1555,02883684960 |
-68,9220732243511 | 70,1893695905364 | 292,020436378185 | 269,134039310842 | 314,307955443979 | 7,84300331362681 | -911,917618688801 | -31,8584266433906 | -77,3980086116821 | 1499,66220700640 | -73,8106741065346 | 458,800686602646 | 34,1849703833048 | 4,18496453253449 | -13,8150417443774 | 185,184949360665 | 118,184938942491 | 120,184920521443 | 153,163037620134 | -46,3369655623850 |
-464,408261445729 | 417,227306683108 | 225,249046624667 | 337,923277544196 | 4422,71615234540 | 7070,19909629300 | -9045,98150781726 | 770,126739966631 | 1499,66220700640 | -7567,92000066924 | -425,995424326623 | -440,931329272520 | 601,021258878684 | 461,521201024281 | -205,978861043955 | -94,4789490003119 | 36,0209479812381 | 52,5207658276643 | 6522,30438026823 | -458,195651201595 |
354,436277014027 | 54,3930231232374 | 313,090918595099 | 187,650409777138 | 51,6602195330760 | -61,8702234704563 | -548,996631399145 | -1,54352369648362 | -73,8106741065346 | -425,995424326623 | -252,552035184705 | -17,9198241941512 | 196,837181949189 | 35,8371713804397 | -40,6628399580857 | 357,337143974189 | -24,1628748450555 | 33,3370918794234 | 272,797562914294 | -83,7024428345629 |
-32,6210091306378 | 1226,29621493700 | 319,761956170420 | 317,296997753149 | 712,108618884869 | 636,731055964564 | -741,232522450841 | 276,986996571434 | 458,800686602646 | -440,931329272520 | -17,9198241941512 | -67,3498058742369 | 104,795873714524 | 1391,79586825674 | 305,795862401438 | 50,7958541039400 | 614,795844385537 | 503,295827201800 | 641,775414138493 | -43,2245888302618 |
737,772968912729 | 44,2756880428884 | 266,348961468383 | 238,503348281279 | 220,458594503794 | 234,453130765985 | 702,313322917668 | 249,059830935245 | 34,1849703833048 | 601,021258878684 | 196,837181949189 | 104,795873714524 | -27,7149503827362 | 3,28504611615824 | 4,78504236004920 | 208,785037037300 | 44,7850308030558 | 21,2850197798864 | 526,771925034422 | -27,7280768700001 |
-40,7270370532508 | 206,275685109065 | 1272,34895500670 | 1269,50334247073 | -33,5414137125955 | -56,5468809250466 | -565,186751006344 | 42,5598226684816 | 4,18496453253449 | 461,521201024281 | 35,8371713804397 | 1391,79586825674 | 3,28504611615824 | -27,7149573849478 | 1680,28503885894 | 2625,28503353619 | 193,285027301948 | 182,285016278777 | 31,7719215316582 | -27,7280803727639 |
-43,7270434537630 | 1219,27568196156 | 142,348948074382 | 206,503336236965 | -32,5414225274268 | -62,5468934675959 | -560,686830314621 | 45,5598137996073 | -13,8150417443774 | -205,978861043955 | -40,6628399580857 | 305,795862401438 | 4,78504236004920 | 1680,28503885894 | -27,7149648971673 | 472,785029780082 | 580,285023545836 | 6012,28501252266 | 23,2719177737704 | -27,7280841306519 |
4,27294747612693 | 2151,77567750125 | 396,348938250654 | 802,003327403153 | 477,958564981153 | 427,953088758467 | -461,186942701689 | 423,559801231603 | 185,184949360665 | -94,4789490003119 | 357,337143974189 | 50,7958541039400 | 208,785037037300 | 2625,28503353619 | 472,785029780082 | -27,7149755426699 | 966,785018223083 | 1562,28500719991 | 436,271912448500 | -27,7280894559223 |
-36,7270631471949 | 102,775672277136 | 693,848926744659 | 506,003317056595 | 232,458550350638 | 143,953067940830 | -550,687074334490 | 108,559786511389 | 118,184938942491 | 36,0209479812381 | -24,1628748450555 | 614,795844385537 | 44,7850308030558 | 193,285027301948 | 580,285023545836 | 966,785018223083 | -27,7149880111650 | 424,285000965658 | 201,771906211304 | -27,7280956931190 |
-34,7270819309761 | 1153,27566304005 | 536,348906400168 | 638,503298762177 | 93,9585244814797 | 1,45303113182250 | -529,687307082946 | 93,5597604836297 | 120,184920521443 | 52,5207658276643 | 33,3370918794234 | 503,295827201800 | 21,2850197798864 | 182,285016278777 | 6012,28501252266 | 1562,28500719991 | 424,285000965658 | -27,7150100575232 | 52,2718951829146 | -27,7281067215093 |
-28,2493957342700 | 149,264690029108 | 693,324738583861 | 638,981566287893 | 334,927793751752 | 239,409304634772 | 14007,0362042176 | 828,028841346297 | 153,163037620134 | 6522,30438026823 | 272,797562914294 | 641,775414138493 | 526,771925034422 | 31,7719215316582 | 23,2719177737704 | 436,271912448500 | 201,771906211304 | 52,2718951829146 | -27,7412057636462 | -27,7412076689699 |
-47,2493989794566 | -23,2353115667414 | -51,1752649309627 | -46,0184368727489 | -65,0722107175426 | -92,5907017245495 | -585,463835993231 | 1555,02883684960 | -46,3369655623850 | -458,195651201595 | -83,7024428345629 | -43,2245888302618 | -27,7280768700001 | -27,7280803727639 | -27,7280841306519 | -27,7280894559223 | -27,7280956931190 | -27,7281067215093 | -27,7412076689699 | -27,7412095742936 |