From 421192b7e528de0993fce6b1974d1a442f0cd370 Mon Sep 17 00:00:00 2001 From: "Claudio Maggioni (maggicl)" Date: Thu, 22 Apr 2021 16:39:35 +0200 Subject: [PATCH] hw3: done all but 1.5 and 2.5 --- Claudio_Maggioni_2/main.m | 2 +- Claudio_Maggioni_3/1-4-grad-large.jpg | Bin 0 -> 52234 bytes Claudio_Maggioni_3/1-4-grad-nonlog.jpg | Bin 0 -> 49740 bytes Claudio_Maggioni_3/1-4-grad.jpg | Bin 0 -> 50170 bytes Claudio_Maggioni_3/1-4-ys-large.jpg | Bin 0 -> 49283 bytes Claudio_Maggioni_3/1-4-ys-nonlog.jpg | Bin 0 -> 51265 bytes Claudio_Maggioni_3/1-4-ys.jpg | Bin 0 -> 50586 bytes Claudio_Maggioni_3/Claudio_Maggioni_3.pdf | Bin 0 -> 524794 bytes Claudio_Maggioni_3/Claudio_Maggioni_3.tex | 147 + Claudio_Maggioni_3/ex1-3-large.tex | 34 - Claudio_Maggioni_3/ex1-3.jpg | Bin 0 -> 62168 bytes Claudio_Maggioni_3/ex1-3.tex | 21191 ------------------- Claudio_Maggioni_3/ex1-4-grad-large.tex | 21165 ------------------- Claudio_Maggioni_3/ex1-4-grad.tex | 21193 -------------------- Claudio_Maggioni_3/ex1-4-ys-large.tex | 36 - Claudio_Maggioni_3/ex1-4-ys.tex | 21193 -------------------- Claudio_Maggioni_3/main.asv | 176 + Claudio_Maggioni_3/main.m | 43 +- 18 files changed, 361 insertions(+), 84819 deletions(-) create mode 100644 Claudio_Maggioni_3/1-4-grad-large.jpg create mode 100644 Claudio_Maggioni_3/1-4-grad-nonlog.jpg create mode 100644 Claudio_Maggioni_3/1-4-grad.jpg create mode 100644 Claudio_Maggioni_3/1-4-ys-large.jpg create mode 100644 Claudio_Maggioni_3/1-4-ys-nonlog.jpg create mode 100644 Claudio_Maggioni_3/1-4-ys.jpg create mode 100644 Claudio_Maggioni_3/Claudio_Maggioni_3.pdf create mode 100755 Claudio_Maggioni_3/Claudio_Maggioni_3.tex delete mode 100644 Claudio_Maggioni_3/ex1-3-large.tex create mode 100644 Claudio_Maggioni_3/ex1-3.jpg delete mode 100644 Claudio_Maggioni_3/ex1-3.tex delete mode 100644 Claudio_Maggioni_3/ex1-4-grad-large.tex delete mode 100644 Claudio_Maggioni_3/ex1-4-grad.tex delete mode 100644 Claudio_Maggioni_3/ex1-4-ys-large.tex 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b/Claudio_Maggioni_3/Claudio_Maggioni_3.tex new file mode 100755 index 0000000..4253e41 --- /dev/null +++ b/Claudio_Maggioni_3/Claudio_Maggioni_3.tex @@ -0,0 +1,147 @@ +\documentclass{scrartcl} +\usepackage{pdfpages} +\usepackage[utf8]{inputenc} +\usepackage{float} +\usepackage{graphicx} +\usepackage[ruled,vlined]{algorithm2e} +\usepackage{subcaption} +\usepackage{hyperref} +\usepackage{amsmath} +\usepackage{pgfplots} +\pgfplotsset{compat=newest} +\usetikzlibrary{plotmarks} +\usetikzlibrary{arrows.meta} +\usepgfplotslibrary{patchplots} +\usepackage{grffile} +\usepackage{amsmath} +\usepackage{subcaption} +\usepgfplotslibrary{external} +\tikzexternalize +\usepackage[margin=2.5cm]{geometry} + +% To compile: +% sed -i 's#title style={font=\\bfseries#title style={yshift=1ex, font=\\tiny\\bfseries#' *.tex +% luatex -enable-write18 -shellescape main.tex + +\pgfplotsset{every x tick label/.append style={font=\tiny, yshift=0.5ex}} +\pgfplotsset{every title/.append style={font=\tiny, align=center}} +\pgfplotsset{every y tick label/.append style={font=\tiny, xshift=0.5ex}} +\pgfplotsset{every z tick label/.append style={font=\tiny, xshift=0.5ex}} + +\setlength{\parindent}{0cm} +\setlength{\parskip}{0.5\baselineskip} + +\title{Optimization methods -- Homework 3} +\author{Claudio Maggioni} + +\begin{document} + +\maketitle + +\section{Exercise 1} + +\subsection{Exercise 1.1} + +Please consult the MATLAB implementation in the files \texttt{Newton.m}, \texttt{GD.m}, and \texttt{backtracking.m}. +Please note that, for this and subsequent exercises, the gradient descent method without backtracking activated uses a +fixed $\alpha=1$ despite the indications on the assignment sheet. This was done in order to comply with the forum post +on iCorsi found here: \url{https://www.icorsi.ch/mod/forum/discuss.php?d=81144}. + +\subsection{Exercise 1.2} + +Please consult the MATLAB implementation in the file \texttt{main.m} in section 1.2. + +\subsection{Exercise 1.3} + +Please find the requested plots in figure \ref{fig:1}. The code used to generate these plots can be found in section 1.3 of \texttt{main.m}. + +\begin{figure}[h] + \begin{subfigure}{0.5\textwidth} + \resizebox{\textwidth}{\textwidth}{\includegraphics{ex1-3.jpg}} + \caption{Zoomed plot on $x = (-1,1)$ and $y = (-1,1)$} + \end{subfigure} + \begin{subfigure}{0.5\textwidth} + \resizebox{\textwidth}{\textwidth}{\input{ex1-3-gd}} + \caption{Complete plot} + \end{subfigure} + \caption{Steps in the energy landscape for Newton and GD methods}\label{fig:1} +\end{figure} + +\subsection{Exercise 1.4} + +Please find the requested plots in figure \ref{fig:gsppn}. The code used to generate these plots can be found in section 1.4 of \texttt{main.m}. + +\begin{figure}[h] + \begin{subfigure}{0.45\textwidth} + \resizebox{\textwidth}{\textwidth}{\includegraphics{1-4-grad-nonlog.jpg}} + \caption{Gradient norms \\(zoomed, y axis is linear for this plot)} + \end{subfigure} + \begin{subfigure}{0.45\textwidth} + \resizebox{\textwidth}{\textwidth}{\includegraphics{1-4-ys-nonlog.jpg}} + \caption{Objective function values \\(zoomed, y axis is linear for this plot)} + \end{subfigure} + \begin{subfigure}{0.45\textwidth} + \resizebox{\textwidth}{\textwidth}{\includegraphics{1-4-grad.jpg}} + \caption{Gradient norms (zoomed)} + \end{subfigure} + \begin{subfigure}{0.45\textwidth} + \resizebox{\textwidth}{\textwidth}{\includegraphics{1-4-ys.jpg}} + \caption{Objective function values (zoomed)} + \end{subfigure} + \begin{subfigure}{0.45\textwidth} + \resizebox{\textwidth}{\textwidth}{\includegraphics{1-4-grad-large.jpg}} + \caption{Gradient norms} + \end{subfigure} + \begin{subfigure}{0.45\textwidth} + \centering + \resizebox{\textwidth}{\textwidth}{\includegraphics{1-4-ys-large.jpg}} + \caption{Objective function values} + \end{subfigure} + \caption{Gradient norms and objective function values (y-axes) w.r.t. iteration numbers (x-axis) for Newton and GD methods (y-axis is log scaled, points at $y=0$ not shown due to log scale)}\label{fig:gsppn} +\end{figure} + +\section{Exercise 1.5} + +TBD + +\section{Exercise 2} + +\subsection{Exercise 2.1} + +Please consult the MATLAB implementation in the file \texttt{BGFS.m}. + +\subsection{Exercise 2.2} + +Please consult the MATLAB implementation in the file \texttt{main.m} in section 2.2. + +\subsection{Exercise 2.3} + +Please find the requested plots in figure \ref{fig:3}. The code used to generate these plots can be found in section 2.3 of \texttt{main.m}. + +\begin{figure}[h] + \centering + \resizebox{.6\textwidth}{.6\textwidth}{\input{ex2-3}} + \caption{Steps in the energy landscape for BGFS method}\label{fig:3} +\end{figure} + +\subsection{Exercise 2.4} + +Please find the requested plots in figure \ref{fig:4}. The code used to generate these plots can be found in section 2.4 of \texttt{main.m}. + +\begin{figure}[h] + \begin{subfigure}{0.5\textwidth}` + \resizebox{\textwidth}{\textwidth}{\input{ex2-4-grad}} + \caption{Gradient norms} + \end{subfigure} + \begin{subfigure}{0.5\textwidth} + \resizebox{\textwidth}{\textwidth}{\input{ex2-4-ys}} + \caption{Objective function values} + \end{subfigure} + \caption{Gradient norms and objective function values (y-axes) w.r.t. iteration numbers (x-axis) for BFGS method (y-axis is log scaled, points at $y=0$ not shown due to log scale)}\label{fig:4} +\end{figure} + +\subsection{Exercise 2.5} + +TBD + +\end{document} diff --git a/Claudio_Maggioni_3/ex1-3-large.tex b/Claudio_Maggioni_3/ex1-3-large.tex deleted file mode 100644 index 4ef822c..0000000 --- a/Claudio_Maggioni_3/ex1-3-large.tex +++ /dev/null @@ -1,34 +0,0 @@ -% This file was created by matlab2tikz. -% -\definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}% -% -\begin{tikzpicture} - -\begin{axis}[% 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