From 98b7349508e279ae85daec00869fedce32d681e9 Mon Sep 17 00:00:00 2001 From: "Claudio Maggioni (maggicl)" Date: Sun, 21 Mar 2021 15:05:22 +0100 Subject: [PATCH] Initial commit --- .gitignore | 150 +++++++++++++++++++++++++++++++++++++++++++++++++++ hw1/ex3.m | 43 +++++++++++++++ hw1/main.pdf | Bin 0 -> 110017 bytes hw1/main.tex | 70 ++++++++++++++++++++++++ 4 files changed, 263 insertions(+) create mode 100755 .gitignore create mode 100644 hw1/ex3.m create mode 100644 hw1/main.pdf create mode 100644 hw1/main.tex diff --git a/.gitignore b/.gitignore new file mode 100755 index 0000000..03ba496 --- /dev/null +++ b/.gitignore @@ -0,0 +1,150 @@ +*.ijvm +*.mic1 + +# ---> TeX +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc + +## Intermediate documents: +*.dvi +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf + +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bcf +*.blg +*-blx.aux +*-blx.bib +*.brf +*.run.xml + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync + +## Auxiliary and intermediate files from other packages: + + +# algorithms +*.alg +*.loa + +# achemso +acs-*.bib + +# amsthm +*.thm + +# beamer +*.nav +*.snm +*.vrb + +#(e)ledmac/(e)ledpar +*.end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls + +# gnuplottex +*-gnuplottex-* + +# hyperref +*.brf + +# knitr +*-concordance.tex +*.tikz +*-tikzDictionary + +# listings +*.lol + +# makeidx +*.idx +*.ilg +*.ind +*.ist + +# minitoc +*.maf +*.mtc +*.mtc[0-9] +*.mtc[1-9][0-9] + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# mylatexformat +*.fmt + +# nomencl +*.nlo + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# TikZ & PGF +*.dpth +*.md5 +*.auxlock + +# todonotes +*.tdo + +# xindy +*.xdy + +# WinEdt +*.bak +*.sav + +# Mac stupid tmp files +.DS_Store + +!*.pdf +*.zip + +**/*-figure*.pdf + +*~ diff --git a/hw1/ex3.m b/hw1/ex3.m new file mode 100644 index 0000000..9d85de0 --- /dev/null +++ b/hw1/ex3.m @@ -0,0 +1,43 @@ +%% Exercise 3.1 + +% f(x1, x2) = x1^2 + u * x2^2; + +% [x1 x2] [1 0] [x1] + [0][x1] +% [0 u] [x2] + [0][x2] + +% A = [1 0; 0 u]; b = [0; 0] + +%% Exercise 3.2 + + +for u = 1:10 + A = [1 0; 0 u]; + + xs = -10:1:10; + ys = xs; + + Z = zeros(size(xs, 2), size(ys, 2)); + + for i = 1:size(xs, 2) + for j = 1:size(ys, 2) + vec = [xs(i); ys(j)]; + Z(i, j) = vec' * A * vec; + end + end + + if u <= 5 + fig = u; + con = 5 + u; + else + fig = 10 + u - 5; + con = 15 + u - 5; + end + + subplot(4, 5, fig); + h = surf(xs, ys, Z); + set(h,'LineStyle','none'); + title(sprintf("Surf for u=%d", u)); + subplot(4, 5, con); + contour(xs, ys, Z, 20); + 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If for example we consider A and b to be only zeros, then $J(x) = 0$ for all $x \in \!R^n$ and thus $J$ would have an infinite number of minimizers. + +However, for if $A$ would be guaranteed to have full rank, the minimizer would be unique because the first order necessary condition would hold only for one value $x^*$. This is because the linear system $Ax^* = b$ would have one and only one solution (due to $A$ being full rank). + +\end{document}