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My assignemt solutions for CMSC764:Numerical Optimization course offererd by the University of Maryland
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cmsc764-advance-numerical-optimization's Introduction
CMSC764-Advance-Numerical-Optimization
Homework 1 : Linear Algebra
- Problem 1 : Prove the dual norm a norm.
- Problem 2 : Proove Convolution Theorem.
- Problem 3 : Prove the Cooley-Tukey factorization formula.
- problem 4 : Derive the negative log-likelihood function for x given y.
Homework 2 : More Linear Algebra
- Problem 1 : Effect of bad condition number.
- Problem 2 : Write a method for checking whether
At
is the adjoint of A
.
- Problem 3 : Implement the adjoint/transpose for convolution operators.
- problem 4 : FFT.
- Problem 1 : Gradient checker.
- Problem 2 : Write a routine that evaluates the logistic loss function.
- Problem 3 : IImplement the total-variation denoising objective.
Homework 4 : PySmorch (A machine learning library for the dregs of society)
- Problem 1 : A linear layer.
- Problem 2 : ReLU layer.
- Problem 3 : Cross Entropy.
- problem 4 : Bias layer.
Homework 5 : Convex Functions
- Problem 1 : Check if the functions are convex.
- Problem 2 : Verify properties of convex functions.
- Problem 3 : Quasi convex
Homework 6 : Gradient methods and Duality
- Problem 1 : Gradient descent: GD, Barzilai-Borwein, Nestrov
- Problem 2 : Image denoising
- Problem 3 : The dual
- Problem 4 : Linear programming example
Homework 7 : Splitting Methods
- Problem 1 : Forward-backward splitting
- Problem 2 : Netflix problem
Homework 8: Alternating Direction Method of Multipliers (ADMM)
Homework 9: Monte Carlo Markov Chain (MCMC)
- Image recovery using Total-Variation denoising objective.
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