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What is the normal cone of the constraints of a quadratically constrained quadratic programming(QCQP)?

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#optimization #semidefinite-programming #convex-cone #qcqp
37
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Prove $\{X\in S^n_+ | \langle A,X \rangle =a, \langle B,X\rangle =b, \langle C,X\rangle =c\}$ is bounded

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#linear-algebra #convex-analysis #inner-products #positive-semidefinite #semidefinite-programming
170
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SDP reformulation with range space constraint

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#optimization #convex-optimization #semidefinite-programming
422
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matrix inner product between positive semidefinite matrix and positive definite matrix

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#linear-algebra #matrices #trace #semidefinite-programming #linear-matrix-inequality
387
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How do I transform this problem into a semidefinite program?

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#optimization #convex-optimization #semidefinite-programming #schur-complement
136
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Efficient algorithm for SDP relaxation of max-cut

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#graph-theory #optimization #convex-analysis #semidefinite-programming #relaxations
797
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Are basic feasible solutions, vertices, and extreme points equivalent for semidefinite programs (SDPs)?

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#optimization #semidefinite-programming
147
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Find $\nabla_x\left\langle L,Z-\begin{bmatrix}Tu&x\\ x^H&t\end{bmatrix}\right\rangle+p/2\left\|Z-\begin{bmatrix}Tu&x\\ x^H&t\end{bmatrix}\right\|^2$

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#complex-numbers #solution-verification #convex-optimization #lagrange-multiplier #semidefinite-programming
188
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How to solve the following quadratic matrix equation?

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#matrix-equations #matrix-decomposition #svd #quadratic-programming #semidefinite-programming
45
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Maximize $\gamma$ such that $A+\lambda B-\gamma C\succeq 0$

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#linear-algebra #convex-optimization #positive-definite #semidefinite-programming
145
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Proving tightness of a semidefinite relaxation of a nonconvex quadratic program

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#matrix-rank #semidefinite-programming #non-convex-optimization #qcqp #relaxations
614
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Conditions for a block matrix to be positive definite

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#linear-algebra #matrices #matrix-equations #positive-definite #semidefinite-programming
226
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Feasibility of Matrix Inequality

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#matrices #convex-optimization #matrix-calculus #semidefinite-programming #linear-matrix-inequality
2k
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QCQP as a SDP or SOCP?

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#convex-optimization #quadratic-programming #semidefinite-programming #qcqp #second-order-cone-programming
207
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On one property of positive semidefinite matrices

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#linear-algebra #matrices #positive-definite #semidefinite-programming #positive-semidefinite

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