# create.solve_sdp: Optimization for fixed-X and Gaussian knockoffs In knockoff: The Knockoff Filter for Controlled Variable Selection

## Description

This function solves the optimization problem needed to create fixed-X and Gaussian SDP knockoffs on the full covariance matrix. This will be more powerful than create.solve_asdp, but more computationally expensive.

## Usage

 1 create.solve_sdp(Sigma, gaptol = 1e-06, maxit = 1000, verbose = FALSE) 

## Arguments

 Sigma positive-definite p-by-p covariance matrix. gaptol tolerance for duality gap as a fraction of the value of the objective functions (default: 1e-6). maxit maximum number of iterations for the solver (default: 1000). verbose whether to display progress (default: FALSE).

## Details

Solves the semidefinite programming problem:

\mathrm{maximize} \; \mathrm{sum}(s) \quad \mathrm{subject} \; \mathrm{to} 0 ≤q s ≤q 1, \; 2Σ - \mathrm{diag}(s) ≥q 0

This problem is solved using the interior-point method implemented in dsdp.

If the matrix Sigma supplied by the user is a non-scaled covariance matrix (i.e. its diagonal entries are not all equal to 1), then the appropriate scaling is applied before solving the SDP defined above. The result is then scaled back before being returned, as to match the original scaling of the covariance matrix supplied by the user.

## Value

The solution s to the semidefinite programming problem defined above.

Other optimization: create.solve_asdp(), create.solve_equi()