jenkins.warをHTTPS(nginx)で公開する場合の設定

・環境
nginx version: nginx/1.7.10
Jenkins 1.598

http {
    ssl_session_cache      shared:SSL:10m;
    ssl_session_timeout    10m;

    include          /etc/nginx/mime.types;
    default_type     application/octet-stream;

    map $uri $loggable {
        ~*\.(js|css|png|jpg|jpeg|gif|ico|woff) 0;
        default 1;
    }

    log_format  ltsv  'time:$time_local\t'
                      'host:$remote_addr\t'
                      'request:$request\t'
                      'status:$status\t'
                      'size:$body_bytes_sent\t'
                      'referer:$http_referer\t'
                      'ua:$http_user_agent\t'
                      'reqtime:$request_time\t'
                      'upsttime:$upstream_response_time';

    access_log  /var/log/nginx/access.log  ltsv if=$loggable;
    keepalive_timeout  65;
    server_tokens off;

    server {
        listen          443 ssl;
        server_name     localhost;
        ssl             on;
        ssl_protocols   TLSv1 TLSv1.1 TLSv1.2;

        client_max_body_size 100m;

        keepalive_timeout 70;

        ssl_certificate        /path/to/ssl_certificate;
        ssl_certificate_key    /path/to/ssl_certificate_key;

        rewrite ^/$            /jenkins/ redirect;
        # Add trailing slash to */jenkins requests.
        rewrite /jenkins$      $scheme://$host$uri/ permanent;

        location /jenkins {
               proxy_pass              http://127.0.0.1:8080/jenkins;
               proxy_redirect          http://             https://;
               proxy_set_header        Host                $host;
               proxy_set_header        X-Real-IP           $remote_addr;
               proxy_set_header        X-Forwarded-For     $proxy_add_x_forwarded_for;
               proxy_set_header        X-Forwarded-Proto   https;
        }
    }
}

proxy_redirectを記述しないと、一部のメニューのリンクがhttp://になる。
設定で対処できるのであれば、対処したい。