AMAT 591 Final Project
算法实现代写 In this project, you will implement optimization algorithms to recover a sparse signal (or vector) x ∗ ∈ R n by solving the LASSO problem
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Due: December 17, 11:59pm. Late submission will not be accepted. 算法实现代写
In this project, you will implement optimization algorithms to recover a sparse signal (or vector) x ∗ ∈ R n by solving the LASSO problem:
(1)
A ∈ R m×n , b ∈ R m are known. λ > 0 is the penalty parameter.
Problem Setup. Let n = 256, m = 64, λ = 10−6 . For any 1 ≤ i ≤ m and 1 ≤ j ≤ n,the (i,j)-th entry of A is given by
Let the true signal satisfy x ∗ i = 1 for i = 12, 35, 38, 129, 136, 150, 170, 207, 232, 243 and x ∗ i = 0 otherwise. In practice, we do not know x ∗ , but only know the measurement vector b generated according to b = Ax∗ . Our goal here is to recover or reconstruct x ∗ from the measurement b by solving the LASSO problem above.
1.Solve the optimization problem in (1) using accelerated proximal gradient method (a.k.a. FISTA) with the iterations for k = 1, 2, . . . , K:
Take the initialization x 0 = x −1 = 0(n), step size tk≡ 0.3, and maximum iteration number K = 105 . Compute and store the objective value f(x k) at each iteration k.
Denote the output of FISTA by xFISTA := x K. 算法实现代写
- Evaluate the relative error for reconstructed signal, i.e.,
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.- Plot a red curve that joins the points (k, f(x k)) for k = 1, . . . , K in log-log scale. Label the x-axis with “Iteration” and the y-axis with “Objective”.
Take the initialization
x 0=z 0=u 0=0(n) , augmentation parameter δ =10−5 ,and maximum iteration number K = 103 . Compute and store the objective value f(x k ) at each iteration k. Denote the output of ADMM by xADMM := x K. To save computational cost, pre-compute and store the matrix (A> A + δI) −1 before iteration starts.
- Evaluate the relative error
- Plot a blue curve that joins the points (k, f(x k )) for k = 1, . . . , K in log-log scale. The curve should be plotted in the same fifigure as that for FISTA.
Submission. 算法实现代写
Please submit a .zip fifile named ”Final yourLASTNAME yourFIRSTNAME” through MyUAlbany Blackboard, which contains three subfifiles:
- The source code for FISTA.
- The source code for ADMM.
- A report (word or pdf fifile) that displays the two relative errors (for FISTA and ADMM, respectively) and the ‘Objective vs. Iteration’ plot.
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