Given a minimization optimization problem of a linear target function over the set of positive semidefinite matrices of some fixed maximal rank, subject to affine constraints, what are (analytical) methods to find lower bounds on the optimal value of that problem? If we had no rank constraints, the answer would be "convex optimization duality", but the rank constraint makes the problem non-convex.
2026-03-20 17:28:46.1774027726
Proving lower bounds on a minimization problem over positive semidefinite matrices with a bounded maximal rank
18 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CONVEX-OPTIMIZATION
- Optimization - If the sum of objective functions are similar, will sum of argmax's be similar
- Least Absolute Deviation (LAD) Line Fitting / Regression
- Check if $\phi$ is convex
- Transform LMI problem into different SDP form
- Can a linear matrix inequality constraint transform to second-order cone constraint(s)?
- Optimality conditions - necessary vs sufficient
- Minimization of a convex quadratic form
- Prove that the objective function of K-means is non convex
- How to solve a linear program without any given data?
- Distance between a point $x \in \mathbb R^2$ and $x_1^2+x_2^2 \le 4$
Related Questions in NON-CONVEX-OPTIMIZATION
- Find largest possible value of $x^2+y^2$ given that $x^2+y^2=2x-2y+2$
- Interesting Global Minimum of a Non-convex Function
- Minimize $x^T A y$, subject to $ x^Ty\geq 0$, where $A=\Phi^T\Phi$ is symmtric and semi-positive definite.
- How should I proceed to solve the below mentioned non-convex optimisation problem?
- Optimization of the sum of a convex and a non-convex function?
- Solution of a semidefinite program with rank at most $k$
- Trace maximization with semi-orthogonal constraint
- Literature on optimizing linear objectives over non-convex sets
- Convex Hull of the Union of Subgradients
- Find matrices $X$ such that the diagonal of $X^H X$ is sparse
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?