CVXR (version 1.0-14)

eye_minus_inv: Unity Resolvent

Description

The unity resolvent of a positive matrix. For an elementwise positive matrix \(X\), this atom represents \((I - X)^{-1}\), and it enforces the constraint that the spectral radius of \(X\) is at most 1.

Usage

eye_minus_inv(X)

Value

An Expression representing the unity resolvent of the input.

Arguments

X

An Expression or positive square matrix.

Details

This atom is log-log convex.

Examples

A <- Variable(2,2, pos = TRUE)
prob <- Problem(Minimize(matrix_trace(A)), list(eye_minus_inv(A) <=1))
result <- solve(prob, gp = TRUE)
result$value
result$getValue(A)