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Pawan Aurora
Pawan Aurora
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Typically the non-empty feasible space of a SDP has some curved regionboundary which is why the feasible space has infinitely many extreme points. Is it ever possible to have a SDP whose non-empty feasible region is the convex hull of a finite (exponential) number of rank-$1$ matrices? If yes, how do we characterize such a SDP? What can we say about the affine hull of these extreme points? Is it somehow related to the affine space defined by the set of equality linear constraints?

Typically the non-empty feasible space of a SDP has some curved region which is why the feasible space has infinitely many extreme points. Is it ever possible to have a SDP whose non-empty feasible region is the convex hull of a finite (exponential) number of rank-$1$ matrices? If yes, how do we characterize such a SDP? What can we say about the affine hull of these extreme points? Is it somehow related to the affine space defined by the set of equality linear constraints?

Typically the non-empty feasible space of a SDP has some curved boundary which is why the feasible space has infinitely many extreme points. Is it ever possible to have a SDP whose non-empty feasible region is the convex hull of a finite (exponential) number of rank-$1$ matrices? If yes, how do we characterize such a SDP? What can we say about the affine hull of these extreme points? Is it somehow related to the affine space defined by the set of equality linear constraints?

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Pawan Aurora
Pawan Aurora
  • 505
  • 3
  • 9

Feasible space of SDP

Typically the non-empty feasible space of a SDP has some curved region which is why the feasible space has infinitely many extreme points. Is it ever possible to have a SDP whose non-empty feasible region is the convex hull of a finite (exponential) number of rank-$1$ matrices? If yes, how do we characterize such a SDP? What can we say about the affine hull of these extreme points? Is it somehow related to the affine space defined by the set of equality linear constraints?