PostfixでRelay access deniedが出る問題について

PostfixでのSMTPサーバーの立ち上げに成功し、ローカルでのメールのやり取りと外部(gmail)から送られてくるメールの受信に成功しました。しかし外部(gmail)への送信がうまく行きません。telnetでアクセスしメール送信を試みると
554 5.7.1 <送信先アドレス>: Relay access denied
というエラーが出ます。
自力で調べたところSMTP認証たるものをしなくてはならないとありましたが、手順がどうも要領を得ず（書いてあることがばらばらで何を信じるべきかよくわからない状態です）質問させていただいた次第です。この問題の解決のため、手順の方向性をご教示いただきたいです。

main.cf

compatibility_level = 2


queue_directory = /var/spool/postfix
command_directory = /usr/bin


daemon_directory = /usr/lib/postfix/bin

data_directory = /var/lib/postfix


mail_owner = postfix

#default_privs = nobody

myhostname = mail.mydomain.com
#myhostname = virtual.domain.tld

mydomain = mydomain.com


#myorigin = $myhostname
myorigin = $mydomain

inet_interfaces = all
#inet_interfaces = $myhostname
#inet_interfaces = $myhostname, localhost


#proxy_interfaces =
#proxy_interfaces = 1.2.3.4


#mydestination = $myhostname, localhost.$mydomain, localhost
mydestination = $myhostname, localhost.$mydomain, localhost, $mydomain
#mydestination = $myhostname, localhost.$mydomain, localhost, $mydomain,
#    mail.$mydomain, www.$mydomain, ftp.$mydomain

#local_recipient_maps = unix:passwd.byname $alias_maps
#local_recipient_maps = proxy:unix:passwd.byname $alias_maps
#local_recipient_maps =

unknown_local_recipient_reject_code = 550

#mynetworks_style = class
#mynetworks_style = 192.168.0.1/24
mynetworks_style = 127.0.0.0/24

mynetworks = 168.100.189.0/28, 127.0.0.0/8
#mynetworks = $config_directory/mynetworks
#mynetworks = hash:/etc/postfix/network_table

relay_domains = $mydestination

# INTERNET OR INTRANET

#relayhost = $mydomain
#relayhost = [gateway.my.domain]
#relayhost = [mailserver.isp.tld]
#relayhost = uucphost
#relayhost = [an.ip.add.ress]


#relay_recipient_maps = hash:/etc/postfix/relay_recipients

#in_flow_delay = 1s



#alias_maps = dbm:/etc/aliases
#alias_maps = hash:/etc/aliases
#alias_maps = hash:/etc/aliases, nis:mail.aliases
#alias_maps = netinfo:/aliases
alias_maps = hash:/etc/postfix/aliases


#alias_database = dbm:/etc/aliases
#alias_database = dbm:/etc/mail/aliases
#alias_database = hash:/etc/aliases
#alias_database = hash:/etc/aliases, hash:/opt/majordomo/aliases
alias_database = $alias_maps


#recipient_delimiter = +

#home_mailbox = Mailbox
#home_mailbox = Maildir/


mail_spool_directory = /srv/mail
#mail_spool_directory = /var/spool/mail


#mailbox_command = /some/where/procmail
#mailbox_command = /some/where/procmail -a "$EXTENSION"

#mailbox_transport = cyrus

#fallback_transport = lmtp:unix:/file/name
#fallback_transport = cyrus
#fallback_transport =

#luser_relay = $user@other.host
#luser_relay = $local@other.host
#luser_relay = admin+$local


header_checks = regexp:/etc/postfix/header_checks

#fast_flush_domains = $relay_domains

smtpd_banner = $myhostname ESMTP 
#smtpd_banner = $myhostname ESMTP $mail_name ($mail_version)


#local_destination_concurrency_limit = 2
#default_destination_concurrency_limit = 20


debug_peer_level = 2


#debug_peer_list = 127.0.0.1
#debug_peer_list = some.domain


debugger_command =
     PATH=/bin:/usr/bin:/usr/local/bin:/usr/X11R6/bin
     ddd $daemon_directory/$process_name $process_id & sleep 5


# debugger_command =
#    PATH=/bin:/usr/bin:/sbin:/usr/sbin; export PATH; screen
#    -dmS $process_name gdb $daemon_directory/$process_name
#    $process_id & sleep 1

# INSTALL-TIME CONFIGURATION INFORMATION
#
# The following parameters are used when installing a new Postfix version.
# 
# sendmail_path: The full pathname of the Postfix sendmail command.
# This is the Sendmail-compatible mail posting interface.
# 
sendmail_path = /usr/bin/sendmail

# newaliases_path: The full pathname of the Postfix newaliases command.
# This is the Sendmail-compatible command to build alias databases.
#
newaliases_path = /usr/bin/newaliases

# mailq_path: The full pathname of the Postfix mailq command.  This
# is the Sendmail-compatible mail queue listing command.
# 
mailq_path = /usr/bin/mailq

# setgid_group: The group for mail submission and queue management
# commands.  This must be a group name with a numerical group ID that
# is not shared with other accounts, not even with the Postfix account.
#
setgid_group = postdrop

# html_directory: The location of the Postfix HTML documentation.
#
html_directory = no

# manpage_directory: The location of the Postfix on-line manual pages.
#
manpage_directory = /usr/share/man

# sample_directory: The location of the Postfix sample configuration files.
# This parameter is obsolete as of Postfix 2.1.
#
sample_directory = /etc/postfix

# readme_directory: The location of the Postfix README files.
#
readme_directory = /usr/share/doc/postfix
inet_protocols = ipv4
meta_directory = /etc/postfix
shlib_directory = /usr/lib/postfix
message_size_limit = 5242880
disable_vrfy_command = yes
smtpd_helo_required = yes
strict_rfc821_envelopes = yes
allow_percent_hack = yes
swap_bangpath = yes
allow_untrusted_routing = no
smtpd_client_restrictions =
   permit_mynetworks,
   reject_unknown_client,
   permit
smtpd_data_restrictions =
   reject_unauth_pipelining,
   reject_multi_recipient_bounce
smtpd_helo_restrictions =
   permit_mynetworks,
   reject_invalid_hostname,
   reject_non_fqdn_hostname,
   reject_unknown_hostname,
   permit
smtpd_sender_restrictions =
   permit_mynetworks,
   reject_unknown_sender_domain,
   reject_non_fqdn_sender,
   permit
smtpd_recipient_restrictions =
   permit_mynetworks,
   reject_non_fqdn_recipient,
   reject_unknown_recipient_domain,
   reject_unauth_destination,
   permit
smtpd_etrn_restrictions =
   permit_mynetworks,
   reject_invalid_hostname,
   permit