METHODS FOR FINDING GLOBAL OPTIMAL SOLUTIONS TO LINEAR PROGRAMS WITH EQUILIBRIUM CONSTRAINTS
LE DUNG MUU, NGUYEN VAN QUY
A mathematical program with equilibrium constraints is an optimization problem with two sets of variables
Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam
Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội
Điện thoại: 024 37563474 - Fax: 024 37564303
Email: vientoan@math.ac.vn
| 1 x Application (90.54%) | 281ms |
| 1 x Booting (9.45%) | 29.32ms |
| Params | |
|---|---|
| 0 | |
| Params | |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| Params | |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| Params | |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| Params | |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| Params | |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| Params | |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| Params | |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
select * from `journals` where `jour_alias` = 'pmethods-for-finding-global-optimalnbspsolutions-to-linear-programsnbspwith-equilibrium-constraintsp' and `jour_year` = '2001' and `jour_exp` = '26' limit 1| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `members` where `name` is null limit 1| Metadata | |
|---|---|
| Backtrace |
|
select * from `pages`| Metadata | |
|---|---|
| Backtrace |
|
select * from `pages`| Metadata | |
|---|---|
| Backtrace |
|
select * from `pages` where `alias` = 'home' limit 1| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `pages` where `alias` = 'home' limit 1| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select `volume` from `issues` group by `volume`| Metadata | |
|---|---|
| Backtrace |
|
select * from `volumes` order by `vol_year` desc| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 50| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 49| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 48| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 47| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 46| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 45| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 44| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 43| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 42| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 41| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 40| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 39| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 38| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 37| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3, 4)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 36| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 35| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 34| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 33| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 32| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 6)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 31| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 30| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 29| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 28| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 27| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 26| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 25| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 24| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2, 3)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 23| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 22| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 21| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 20| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 19| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 18| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 17| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 16| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 15| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 14| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 13| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 12| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 11| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 10| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 9| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 8| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 7| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 6| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 5| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 4| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 3| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 2| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
select * from `issues` where `volume` = 1| Metadata | |
|---|---|
| Bindings |
|
| Backtrace |
|
select * from `issues_types` where `issues_types`.`id` in (1, 2)| Metadata | |
|---|---|
| Backtrace |
|
200
[]
[]
0 of 0array:15 [▼ "accept-encoding" => array:1 [▶ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [▶ 0 => "document" ] "sec-fetch-user" => array:1 [▶ 0 => "?1" ] "sec-fetch-mode" => array:1 [▶ 0 => "navigate" ] "sec-fetch-site" => array:1 [▶ 0 => "none" ] "accept" => array:1 [▶ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [▶ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [▶ 0 => "1" ] "sec-ch-ua-platform" => array:1 [▶ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [▶ 0 => "?0" ] "sec-ch-ua" => array:1 [▶ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [▶ 0 => "no-cache" ] "pragma" => array:1 [▶ 0 => "no-cache" ] "connection" => array:1 [▶ 0 => "keep-alive" ] "host" => array:1 [▶ 0 => "beta.math.ac.vn" ] ]
0 of 0array:41 [▼ "USER" => "www-data" "HOME" => "/var/www" "HTTP_ACCEPT_ENCODING" => "gzip, deflate, br, zstd" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_CONNECTION" => "keep-alive" "HTTP_HOST" => "beta.math.ac.vn" "REDIRECT_STATUS" => "200" "SERVER_NAME" => "beta.math.ac.vn" "SERVER_PORT" => "443" "SERVER_ADDR" => "119.17.215.180" "REMOTE_PORT" => "37512" "REMOTE_ADDR" => "18.218.121.8" "SERVER_SOFTWARE" => "nginx/1.18.0" "GATEWAY_INTERFACE" => "CGI/1.1" "HTTPS" => "on" "REQUEST_SCHEME" => "https" "SERVER_PROTOCOL" => "HTTP/1.1" "DOCUMENT_ROOT" => "/var/www/math.ac.vn/html/public" "DOCUMENT_URI" => "/index.php" "REQUEST_URI" => "/acta/2001-volume26/3/pmethods-for-finding-global-optimalnbspsolutions-to-linear-programsnbspwith-equilibrium-constraintsp" "SCRIPT_NAME" => "/index.php" "CONTENT_LENGTH" => "" "CONTENT_TYPE" => "" "REQUEST_METHOD" => "GET" "QUERY_STRING" => "" "SCRIPT_FILENAME" => "/var/www/math.ac.vn/html/public/index.php" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/index.php" "REQUEST_TIME_FLOAT" => 1743956016.1233 "REQUEST_TIME" => 1743956016 ]
[]
0 of 0array:5 [▼ "content-type" => array:1 [▶ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [▶ 0 => "no-cache, private" ] "date" => array:1 [▶ 0 => "Sun, 06 Apr 2025 16:13:36 GMT" ] "set-cookie" => array:2 [▶ 0 => "XSRF-TOKEN=eyJpdiI6Ii91SjlOeU5jQXJUak90RjBWSFZiRXc9PSIsInZhbHVlIjoiTjZaeWIzNXRDeVVUcDNCMC9YYzNMQ3hNMnBaTUY0byt3RnpKYjRLK2pwVWJXNWgrZ2pHdFIyR2E5Q1dDMVNWZ0h0SDkrYlRwKzVJRC9aV0FCQzdndUlnWVh1T3JCRjdWTThPT1puS0lyVFplV2V1bmpnRU9HK1JKT1o3UHZyNmwiLCJtYWMiOiI1ZTY1MjA4YmMzYWMxZmIxY2RjZmY5NDA3ODk3NzNhZjBkNGQ2MTU0Y2VhYjdiMzkwZDQ0ODhiNTEyODU5MGRlIiwidGFnIjoiIn0%3D; expires=Sun, 06-Apr-2025 18:13:36 GMT; Max-Age=7200; path=/; samesite=lax ◀XSRF-TOKEN=eyJpdiI6Ii91SjlOeU5jQXJUak90RjBWSFZiRXc9PSIsInZhbHVlIjoiTjZaeWIzNXRDeVVUcDNCMC9YYzNMQ3hNMnBaTUY0byt3RnpKYjRLK2pwVWJXNWgrZ2pHdFIyR2E5Q1dDMVNWZ0h0SDkrY ▶" 1 => "laravel_session=eyJpdiI6InoxV3BOUHBpRllrVHdsVFVpR3JrUXc9PSIsInZhbHVlIjoiTEpPa2t0Q1JrU0R2QlFta25TeFkyMzZhTmpPMGlGMkV4azcyU1lQM3RlYTZGd0dxWml0d3BiQmZnRFdGM0VEODFpQ3VCUjdmL1BmTDl0RFhaZ3Z0Tk9aUU1pVGM2L2M3ekMxVmNDSUxFSDE3TVRVdEdWY2dHQnJFeFUzbWpIbVkiLCJtYWMiOiI5YTdmNjYwNGEyMjgyMjI5MGMwNzJmZWNmMWQ5MGRiNWU1MTJjNzhhYjIzM2NlYTBhMDk2YWYyODYxOTZjZGYzIiwidGFnIjoiIn0%3D; expires=Sun, 06-Apr-2025 18:13:36 GMT; Max-Age=7200; path=/; httponly; samesite=lax ◀laravel_session=eyJpdiI6InoxV3BOUHBpRllrVHdsVFVpR3JrUXc9PSIsInZhbHVlIjoiTEpPa2t0Q1JrU0R2QlFta25TeFkyMzZhTmpPMGlGMkV4azcyU1lQM3RlYTZGd0dxWml0d3BiQmZnRFdGM0VEODFp ▶" ] "Set-Cookie" => array:2 [▶ 0 => "XSRF-TOKEN=eyJpdiI6Ii91SjlOeU5jQXJUak90RjBWSFZiRXc9PSIsInZhbHVlIjoiTjZaeWIzNXRDeVVUcDNCMC9YYzNMQ3hNMnBaTUY0byt3RnpKYjRLK2pwVWJXNWgrZ2pHdFIyR2E5Q1dDMVNWZ0h0SDkrYlRwKzVJRC9aV0FCQzdndUlnWVh1T3JCRjdWTThPT1puS0lyVFplV2V1bmpnRU9HK1JKT1o3UHZyNmwiLCJtYWMiOiI1ZTY1MjA4YmMzYWMxZmIxY2RjZmY5NDA3ODk3NzNhZjBkNGQ2MTU0Y2VhYjdiMzkwZDQ0ODhiNTEyODU5MGRlIiwidGFnIjoiIn0%3D; expires=Sun, 06-Apr-2025 18:13:36 GMT; path=/ ◀XSRF-TOKEN=eyJpdiI6Ii91SjlOeU5jQXJUak90RjBWSFZiRXc9PSIsInZhbHVlIjoiTjZaeWIzNXRDeVVUcDNCMC9YYzNMQ3hNMnBaTUY0byt3RnpKYjRLK2pwVWJXNWgrZ2pHdFIyR2E5Q1dDMVNWZ0h0SDkrY ▶" 1 => "laravel_session=eyJpdiI6InoxV3BOUHBpRllrVHdsVFVpR3JrUXc9PSIsInZhbHVlIjoiTEpPa2t0Q1JrU0R2QlFta25TeFkyMzZhTmpPMGlGMkV4azcyU1lQM3RlYTZGd0dxWml0d3BiQmZnRFdGM0VEODFpQ3VCUjdmL1BmTDl0RFhaZ3Z0Tk9aUU1pVGM2L2M3ekMxVmNDSUxFSDE3TVRVdEdWY2dHQnJFeFUzbWpIbVkiLCJtYWMiOiI5YTdmNjYwNGEyMjgyMjI5MGMwNzJmZWNmMWQ5MGRiNWU1MTJjNzhhYjIzM2NlYTBhMDk2YWYyODYxOTZjZGYzIiwidGFnIjoiIn0%3D; expires=Sun, 06-Apr-2025 18:13:36 GMT; path=/; httponly ◀laravel_session=eyJpdiI6InoxV3BOUHBpRllrVHdsVFVpR3JrUXc9PSIsInZhbHVlIjoiTEpPa2t0Q1JrU0R2QlFta25TeFkyMzZhTmpPMGlGMkV4azcyU1lQM3RlYTZGd0dxWml0d3BiQmZnRFdGM0VEODFp ▶" ] ]
0 of 0array:4 [▼ "_token" => "cNTmDYnYVoKUHnSvntfTPqgcKsSa7VxJERWfADoe" "_previous" => array:1 [▶ "url" => "https://beta.math.ac.vn/acta/2001-volume26/3/pmethods-for-finding-global-optimalnbspsolutions-to-linear-programsnbspwith-equilibrium-constraintsp" ] "_flash" => array:2 [▶ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]