¿Por qué no se actualiza Composer?

Estoy usando Ubuntu 16.04 LTS amd64. He instalado LAMP (php5.6, apache2, mysql) y Composer. Descargué mi proyecto laravel de github. Me gustaría actualizar Composer para iniciar el servidor local php artisan serve. Pero cuando me gustaría correr localhost, el terminal dice:

heartprogrammer@heartprogrammer-desktop:/var/www/kstu$ php artisan serve
PHP Warning:  require(/var/www/kstu/bootstrap/../vendor/autoload.php): failed to open stream: No such file or directory in /var/www/kstu/bootstrap/autoload.php on line 17
PHP Fatal error:  require(): Failed opening required '/var/www/kstu/bootstrap/../vendor/autoload.php' (include_path='.:/usr/share/php') in /var/www/kstu/bootstrap/autoload.php on line 17

Intenté actualizar Composer pero dice:

heartprogrammer@heartprogrammer-desktop:/var/www/kstu$ composer update
Loading composer repositories with package information
Updating dependencies (including require-dev)
Your requirements could not be resolved to an installable set of packages.

  Problem 1
    - phpunit/phpunit 4.8.9 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.8 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.7 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.6 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.5 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.4 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.3 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.26 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.25 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.24 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.23 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.22 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.21 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.20 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.2 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.19 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.18 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.17 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.16 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.15 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.14 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.13 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.12 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.11 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.10 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.8.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.7.7 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.7.6 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.7.5 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.7.4 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.7.3 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.7.2 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.7.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.7.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.9 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.8 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.7 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.6 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.5 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.4 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.3 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.2 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.10 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.6.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.5.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.5.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.4.5 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.4.4 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.4.3 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.4.2 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.4.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.4.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.3.5 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.3.4 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.3.3 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.3.2 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.3.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.3.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.2.6 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.2.5 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.2.4 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.2.3 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.2.2 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.2.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.2.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.1.6 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.1.5 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.1.4 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.1.3 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.1.2 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.1.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.1.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.9 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.8 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.7 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.6 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.5 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.4 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.3 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.20 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.2 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.19 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.18 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.17 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.16 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.15 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.14 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.13 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.12 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.11 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.10 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.1 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - phpunit/phpunit 4.0.0 requires ext-dom * -> the requested PHP extension dom is missing from your system.
    - Installation request for phpunit/phpunit ~4.0 -> satisfiable by phpunit/phpunit[4.0.0, 4.0.1, 4.0.10, 4.0.11, 4.0.12, 4.0.13, 4.0.14, 4.0.15, 4.0.16, 4.0.17, 4.0.18, 4.0.19, 4.0.2, 4.0.20, 4.0.3, 4.0.4, 4.0.5, 4.0.6, 4.0.7, 4.0.8, 4.0.9, 4.1.0, 4.1.1, 4.1.2, 4.1.3, 4.1.4, 4.1.5, 4.1.6, 4.2.0, 4.2.1, 4.2.2, 4.2.3, 4.2.4, 4.2.5, 4.2.6, 4.3.0, 4.3.1, 4.3.2, 4.3.3, 4.3.4, 4.3.5, 4.4.0, 4.4.1, 4.4.2, 4.4.3, 4.4.4, 4.4.5, 4.5.0, 4.5.1, 4.6.0, 4.6.1, 4.6.10, 4.6.2, 4.6.3, 4.6.4, 4.6.5, 4.6.6, 4.6.7, 4.6.8, 4.6.9, 4.7.0, 4.7.1, 4.7.2, 4.7.3, 4.7.4, 4.7.5, 4.7.6, 4.7.7, 4.8.0, 4.8.1, 4.8.10, 4.8.11, 4.8.12, 4.8.13, 4.8.14, 4.8.15, 4.8.16, 4.8.17, 4.8.18, 4.8.19, 4.8.2, 4.8.20, 4.8.21, 4.8.22, 4.8.23, 4.8.24, 4.8.25, 4.8.26, 4.8.3, 4.8.4, 4.8.5, 4.8.6, 4.8.7, 4.8.8, 4.8.9].

  To enable extensions, verify that they are enabled in those .ini files:
    - /etc/php/5.6/cli/php.ini
    - /etc/php/5.6/cli/conf.d/10-opcache.ini
    - /etc/php/5.6/cli/conf.d/10-pdo.ini
    - /etc/php/5.6/cli/conf.d/20-calendar.ini
    - /etc/php/5.6/cli/conf.d/20-ctype.ini
    - /etc/php/5.6/cli/conf.d/20-exif.ini
    - /etc/php/5.6/cli/conf.d/20-fileinfo.ini
    - /etc/php/5.6/cli/conf.d/20-ftp.ini
    - /etc/php/5.6/cli/conf.d/20-gettext.ini
    - /etc/php/5.6/cli/conf.d/20-iconv.ini
    - /etc/php/5.6/cli/conf.d/20-json.ini
    - /etc/php/5.6/cli/conf.d/20-mbstring.ini
    - /etc/php/5.6/cli/conf.d/20-mcrypt.ini
    - /etc/php/5.6/cli/conf.d/20-phar.ini
    - /etc/php/5.6/cli/conf.d/20-posix.ini
    - /etc/php/5.6/cli/conf.d/20-readline.ini
    - /etc/php/5.6/cli/conf.d/20-shmop.ini
    - /etc/php/5.6/cli/conf.d/20-sockets.ini
    - /etc/php/5.6/cli/conf.d/20-sysvmsg.ini
    - /etc/php/5.6/cli/conf.d/20-sysvsem.ini
    - /etc/php/5.6/cli/conf.d/20-sysvshm.ini
    - /etc/php/5.6/cli/conf.d/20-tokenizer.ini
  You can also run `php --ini` inside terminal to see which files are used by PHP in CLI mode.
heartprogrammer@heartprogrammer-desktop:/var/www/kstu$

Las extensiones están habilitadas desde /etc/php/5.6/apache2/php.ini.

extension=php_bz2.dll
extension=php_curl.dll
extension=php_fileinfo.dll
extension=php_gd2.dll
extension=php_gettext.dll
extension=php_gmp.dll
extension=php_intl.dll
extension=php_imap.dll
extension=php_interbase.dll
extension=php_ldap.dll
extension=php_mbstring.dll
extension=php_exif.dll      ; Must be after mbstring as it depends on it
extension=php_mysql.dll
extension=php_mysqli.dll
extension=php_oci8_12c.dll  ; Use with Oracle Database 12c Instant Client
extension=php_openssl.dll
extension=php_pdo_firebird.dll
extension=php_pdo_mysql.dll
extension=php_pdo_oci.dll
extension=php_pdo_odbc.dll
extension=php_pdo_pgsql.dll
extension=php_pdo_sqlite.dll
extension=php_pgsql.dll
extension=php_shmop.dll

; The MIBS data available in the PHP distribution must be installed.
; See http://www.php.net/manual/en/snmp.installation.php
extension=php_snmp.dll

extension=php_soap.dll
extension=php_sockets.dll
extension=php_sqlite3.dll
extension=php_sybase_ct.dll
extension=php_tidy.dll
extension=php_xmlrpc.dll
extension=php_xsl.dll

¿Qué estoy haciendo mal?

Necesita instalar la extensión php dom.

sudo apt-get install php-xml

Pero como todavía estás usando php5.6 ...

sudo apt-get install php5.6-xml

.. hará el truco.

Uno podría instalar los paquetes requeridos 1 por 1. Pero para facilitar la vida intente

sudo apt-get install php5.6-*

esto instalará todo lo relacionado con php5.6

Necesita instalar php5.6-xml sudo apt-get install -y php5.6-xmly composer update. Lo más probable es que también te falte mbstring. Si recibe el error, instale este paquete también con:sudo apt-get install php-mbstring