Quadratic programming is the process of solving a special type of mathematical optimization problem—specifically, a quadratic optimization problem, that is, the problem of optimizing a quadratic function of several variables subject to linear constraints on these variables. Quadratic programming is a particular type of nonlinear programming; the quadratic programming problem with n variables and m constraints can be formulated. Given: a real-valued, n-dimensional vector c, an n × n-dimensional real symmetric matrix Q, an m × n-dimensional real matrix A, an m-dimensional real vector b,the objective of quadratic programming is to find an n-dimensional vector x, that will where xT denotes the vector transpose of x; the notation Ax ⪯ b means that every entry of the vector Ax is less than or equal to the corresponding entry of the vector b. A related programming problem, quadratically constrained quadratic programming, can be posed by adding quadratic constraints on the variables. For general problems a variety of methods are used, including interior point, active set, augmented Lagrangian, conjugate gradient, gradient projection, extensions of the simplex algorithm.

In the case in which Q is positive definite, the problem is a special case of the more general field of convex optimization. Quadratic programming is simple when Q is positive definite and there are only equality constraints. By using Lagrange multipliers and seeking the extremum of the Lagrangian, it may be shown that the solution to the equality constrained problem Minimize 1 2 x T Q x + c T x subject to E x = d is given by the linear system = where λ is a set of Lagrange multipliers which come out of the solution alongside x; the easiest means of approaching this system is direct solution, which for small problems is practical. For large problems, the system poses some unusual difficulties, most notably that the problem is never positive definite, making it very difficult to find a good numeric approach, there are many approaches to choose from dependent on the problem. If the constraints don't couple the variables too a simple attack is to change the variables so that constraints are unconditionally satisfied.

For example, suppose d = 0. Looking at the constraint equations: E x = 0 introduce a new variable y defined by Z y = x where y has dimension of x minus the number of constraints. E Z y = 0 and if Z is chosen so that E Z = 0 the constraint equation will be always satisfied. Finding such Z entails finding the null space of E, more or less simple depending on the structure of E. Substituting into the quadratic form gives an unconstrained minimization problem: 1 2 x T Q x + c T x ⇒ 1 2 y T Z T Q Z y + T y the solution of, given by: Z T Q Z y = − Z T c Under certain conditions on Q, the reduced matrix Z T Q Z will be positive definite, it is possible to write a variation on the conjugate gradient method which avoids the explicit calculation of Z. The Lagrangian dual of a QP is a QP. To see that let us focus on the case where c = 0 and Q is positive definite. We write the Lagrangian function as L ( x

The Indian desert jird or Indian desert gerbil is a species of jird found in the Thar Desert in India. Jirds are related to gerbils; the Indian desert jird is found in southeastern Pakistan to northwestern India. In India they can be found in Gujarat; the Indian desert jird has a grey-brown coat with yellowish-grey belly. It is 12–14 centimetres long and has a tail 10–15 cm long; the distinguishing characteristics include long black claws and orange incisors. Jirds inhabit desert and barren areas preferring firm soil, they are not to be found in rocky outcrops. The jirds are gregarious and their burrows are seen close by; each jird will have more entrances to his burrow complex. The entrance is in the shade of a tree or near the trunk of bushes, they feed on seeds, nuts and insects. Jirds are related to gerbils but can be distinguished by the lack of long hind feet and the characteristic erect posture of a gerbil; the tail of a jird is shorter than the head and body. It has much shorter ears. In addition, the Indian desert jird is diurnal, in comparison to the three common gerbil species found in India which are nocturnal.

Menon, Vivek. A Field Guide to Indian Mammals. Dorling Kindersley, Delhi, 2003. Indian hairy-footed gerbil - gerbil-info.com Media related to Meriones hurrianae at Wikimedia Commons

The 2020 Commission Report on the North Korean Nuclear Attacks Against the United States is a speculative fiction novel by Jeffrey Lewis describing a hypothetical nuclear attack by North Korea against the United States of America, published by Mariner Books. It is written in the style of a government report written in the aftermath of the conflict, in 2023, uses many real-world figures; the conflict begins unintentionally, with a North Korean KN-06 unit in Ongjin, near the Korean Demilitarized Zone shooting down a civilian Air Busan Airbus A320, flying off-course and without a transponder due to a brief loss of power in the cockpit, having mistaken it for a U. S. stealth aircraft. South Korean President Moon Jae-in orders a retaliatory attack on North Korea without the approval of the United States, firing six missiles at the Headquarters of the Korean People's Army Air and Anti-Air Force near Pyongyang and a residence of Kim Jong-un. Following the missile attack, North Korea's leadership, lacking communications infrastructure, misinterprets Tweets from U.

S. President Donald Trump so as to believe. North Korea launches nuclear missiles in the hopes of staving off further U. S.-South Korean attacks, with nuclear bombs detonating over Seoul, Busan and Daegu in South Korea and Tokyo and Yokohama in Japan. Missiles launched at Guam and Okinawa fail to reach their targets. Negotiations in New York City fail to resolve the conflict; the United States launches a retaliatory conventional strike on North Korea, but fail to locate the vehicle-mobile intercontinental ballistic missiles in North Korea's arsenal. North Korea proceeds to launch 13 nuclear-tipped missiles at the United States; the Ground-Based Interceptors at Fort Greely fail to intercept the incoming ICBMs, which detonate over Honolulu, Jupiter, Arlington County and Manhattan, New York. President Trump evacuates from Mar-a-Lago aboard Air Force One, narrowly avoiding the nuclear explosion. Kim Jong-un subsequently commits suicide at a bunker in Myohyangsan, Mike Pence succeeds Trump as President of the United States.

American President Donald Trump - Trump spends most of the events of the novel at Mar-a-Lago, unintentionally sparking the conflict by causing Kim Jong-un to believe that North Korea's leadership is being targeted. White House Chief of Staff Jack Francis - A retired United States Marine Corps General modeled on John F. Kelly. National Security Advisor Keith Kellogg - In the novel, Kellogg replaced John R. Bolton as National Security Advisor. Secretary of Defense Jim Mattis - Mattis functionally removes consideration of the use of nuclear weapons against North Korea, orchestrates much of the war effort against North Korea. Mattis is depicted as the sole remaining member of Trump's initial inner circle. United States Ambassador to the United Nations Nikki Haley - Haley leads failed negotiations with Ma Zhaoxu, the Permanent Representative of China to the United Nations, to end China's support for North Korea. North Korean Kim Jong-un - The leader of North Korea. Kim misinterprets the South Korean retaliatory attack and Donald Trump's tweets as the beginning of a general war, so he launches an initial strike in the hopes of preventing further attacks on North Korea.

When that fails, Kim launching his remaining nuclear arsenal. He commits suicide when U. S. and South Korean special forces attack his bunker. Ja Song-nam - North Korea's Permanent representative to the United Nations. During the crisis, Ja is unable to contact North Korea's leadership due to damage to the telecommunications grid, he and the rest of the North Korean Mission to the United Nations defects in New Jersey. South Korean President Moon Jae-in - Infuriated by the destruction of BX 411, Moon authorizes a limited retaliatory strike against North Korea, acting without American approval, he is subsequently killed in a nuclear explosion while traveling from the Blue House to the Central Government Complex. Minister of National Defense Jeong Kyeong-doo - Jeong advocates a hardline approach to North Korea following the shoot-down of a civilian airliner, he is killed in the nuclear explosion above Seoul. Chief Presidential Secretary Im Jong-seok - Im provides the point of view for many of the South Korean developments, having narrowly survived the nuclear attack on Seoul in the Blue House.

Lewis drew inspiration from John Hersey's reporting on the atomic bombing of Hiroshima when depicting the casualties of nuclear war. The book received positive reviews, with Julian Borger of The Guardian comparing it to nuclear war stories Dr. Strangelove and On the Beach; the Economist observed that "The terrifying thing about “The 2020 Commission Report” is how much of it is real". The Los Angeles Review of Books described it as "the gut punch everyone needs"; the 2020 Commission Report on the North Korean Nuclear Attacks Against the United States title listing at the Internet Speculative Fiction Database

The Junior Offshore Group is a UK based yacht club that organises offshore yacht races in the UK using IRC handicap system. The upper IRC limit for JOG is set at 1.200 and there is no lower limit as long as yachts comply with the relevant World Sailing Organisation Special Regulations category. Aimed at smaller yachts, though the size of the smallest yacht keeps getting bigger as the years go by. In the UK racing is from the JOG startline off Cowes and races are Cross Channel (Cherbourg, St Vaast, Alderney, Le Havre, St Peter Port etc. or inshore. JOG offers close competitive racing with fantastic company both off the water. A large majority of the races end with a social event organised at the race destination to allow racers the chance to unwind and discuss their race stories. JOG fleets and racing exist in countries such as Australia centered in the capital cities; some State yachting authorities there have separate JOG sub-committees to organise events across a number of participating Clubs.

The JOG was founded 7 December 1950 at the Royal Ocean Racing Club. Its first President was the yacht designer John Illingworth. Official website

Jaron Johnson is an American professional basketball player for Élan Chalon of the LNB Pro A. He played college basketball for Tyler Junior Louisiana Tech. Johnson attended John Tyler High School in Tyler, where as a senior in 2009–10, he averaged 17 points and eight rebounds per game, he was subsequently picked as MVP and Offensive Player of the Year in district-5A, named All-East Texas MVP by the Tyler Courier-Times. He was named MVP of the 2010 Azalea Orthopedics Boys all-star game; as a freshman at Tyler Junior College in 2010–11, Johnson averaged 9.9 points, 4.5 rebounds and 1.5 assists per game, as the Apache went 19–11 and made an appearance in the Region XIV Tournament. As a sophomore in 2011–12, Johnson played in all 30 games and averaged 13.2 points, 6.6 rebounds and 2.8 assists per game. He was named first-team all-conference and all-region, led the Apache to an 18–12 record and a quarter-final appearance in the Region XIV Tournament. On April 26, 2012, Johnson signed a National Letter of Intent with the Louisiana Tech Bulldogs.

As a junior in 2012–13, Johnson played in all 34 games for the Bulldogs and averaged 4.6 points and 2.9 rebounds per game. He had his most productive outing against Seattle on January 19, 2013 with a career-high 15 points on 4-of-10 shooting and a career-high eight rebounds; as a senior in 2013–14, Johnson played in 34 games with 18 starts, including the last 16 games, while averaging 9.1 points in 21.5 minutes per game. He recorded double-digit scoring games 18 times while being the leading scorer in five games, he finished 12th in Conference USA in field goal shooting percentage. He registered a lone double-double against FIU on January 11, 2014 with career highs in points and rebounds, he matched his career high in points with 18 against Tulsa on February 6. After going undrafted in the 2014 NBA draft, Johnson tried out with the Rio Grande Valley Vipers of the NBA Development League in October 2014, his try-out was successful and he made the Vipers' 2014–15 training camp roster. His form during preseason earned him a spot on the Vipers' opening-day roster, he made his D-League debut on November 14, 2014 against the Austin Spurs, scoring five points in 15 minutes off the bench.

He emerged as a valuable contributor for the Vipers, evolving from a reserve playing spotty minutes to a reliable starter. Johnson was slotted as an energy guy off the bench, but with the Vipers' offense struggling a month into the season, coach Nevada Smith turned to Johnson because of his aggressiveness and intensity. On February 4, 2015, Johnson scored a career-high 35 points on 11-of-17 shooting in a 130–113 win over the Oklahoma City Blue; the Vipers finished the regular season with a 27–23 record, missing a playoff berth in the Western Conference. Johnson appeared in all 50 games for the Vipers in 2014–15, making 38 starts and averaging 15.1 points, 4.5 rebounds and 1.7 assists per game. In July 2015, Johnson joined the Houston Rockets for the Las Vegas Summer League. In five games for the Rockets, he averaged 1.6 rebounds and 1.0 steals per game. On September 25, 2015, he signed with the Washington Wizards, but was waived by the team on October 24 after appearing in six preseason games.

On November 2, 2015, Johnson was reacquired by the Rio Grande Valley Vipers. In 2015–16, he established himself as one of the better two-way guards in the D-League, evolved into an all-around offensive player, he became a sound facilitator in his second year. Johnson and teammate Will Cummings led the Vipers in scoring. On November 27, in just the fifth game of the season, Johnson scored a season-high 30 points in a 123–108 overtime win over the Los Angeles D-Fenders. On February 6, 2016, he tied his season high of 30 points, this time in a 126–112 loss to the D-Fenders; the Vipers finished the regular season with a 29–21 record, entering the playoffs as the third seed in the Western Conference. In the first round of the playoffs, the Vipers faced the Austin Spurs, but despite going up 1–0 in the series, they went on to lose the next two games to bow out of the playoffs with a 2–1 defeat. Johnson had his best effort of the series in Game 2, scoring 19 points. In 53 games for the Vipers in 2015–16, he averaged 18.1 points, 5.6 rebounds, 3.0 assists and 1.1 steals per game.

On June 28, 2016, Johnson was named in the Indiana Pacers' rookie/free agent camp roster, joining the team for the Orlando Summer League. In four games for the Pacers, he averaged 2.5 rebounds per game. He joined the NBA D-League Select Team for the Las Vegas Summer League, where in four games, he averaged 11.3 points, 5.3 rebounds and 3.0 assists per game. On July 22, 2016, Johnson signed with the Perth Wildcats for the 2016–17 NBL season. After a less-than-impressive debut for the Wildcats, in which he scored six points off the bench in a loss to the Brisbane Bullets in Brisbane on October 6, Johnson turned it around two days in Perth's home opener against the Cairns Taipans. While he struggled to make an impact over the first three quarters, Johnson scored 16 points in the fourth quarter and hit a game-tying three-pointer to send the game into overtime. In overtime, he hit another three-pointer to finish the game with 26 points on 10-of-11 shooting, as he led the Wildcats to an 84–74 win.

However, after scoring just five points in the following game on October 14, Johnson was released by the Wildcats on October 17. Despite being released, he remained in Perth and continued to train with the team while working out with the assistant coaches, his replacement, Andre Ingram, played just two games for the Wildcats before leaving the club after one week. As a result, the Wildcats reactivated Johnson's contract on October 27 ahead of R

Laura Gallego García, is a Spanish author of young adult literature. Laura Gallego García was born in Quart de Poblet, Valencia, on the 11 of October 1977, she is a Spanish novelist of children and juvenile literature, specializing in the fantasy genre. She studied Hispanic Philology at the University of Valencia. At age 11, she started writing ‘Zodiaccía, a different world’, she spent ten years finishing it and, although it has never been published, she has a special affection for this story. She was sure about being a novelist and she sent her work to several literary contests for years. At the age of 21, after finishing high school, she decided to study Hispanic Philology in the University of Valencia, she continued sending her work to publishing houses and contests but she did not publish anything until she wrote ‘Finis Mundi’, the first book she published. She wrote 13 books but none of them were brought to light. With ‘Finis Mundi’, the novelist won the ‘Barco de Vapor’ Prize in 1999 after having participated for several years.

This contest is celebrated every year by SM publishing house. After the publishing of her story'Finis Mundi', she continued with other stories such as'Mandrágora' or the tetralogy of'Crónicas de la Torre'. However, although her fame is due to her juvenile novel, she has published stories aimed at children. In 2002, she won this contest again, this time with her novel ‘La leyenda del rey errante’. In collaboration with SM publishing house, she has published ‘El coleccionista de relojes extraordinarios’, the trilogy of ‘Memorias de Idhún’, ‘Donde los árboles cantan’, ‘Dos velas para el diablo’, the saga of ‘Crónicas de la Torre’ and ‘Las hijas de Tara’, this last one as part of the collection “Gran Angular”. In 2004, she started publishing her second trilogy, called ‘Memorias de Idhún’; this was her biggest success, with more than 750 000 copies sold. She founded the university magazine ‘Náyade’, distributed by the Faculty of Philology at the University of Valencia, she was the co-director from 1997 to 2010.

Afterwards, she has published several independent books, most of them in the fantasy genre, as well as the second part of ‘Alas de fuego’, entitled ‘Alas negras’. She has entered the realist literature with the serie «Sara y las goleadoras», which includes titles such as: ‘Creando equipo’, ‘Las chicas somos guerreras’, ‘Goleadoras en la liga’, ‘El fútbol y el amor son incompatibles’, ‘Las Goleadoras no se rinden’ and ‘El último gol’, her novel ‘Donde los árboles cantan’, published in October 2011, won the ‘Premio Nacional de Literatura Infantil y Juvenil’ in 2012. She has won the ‘Cervantes Chico’ Prize; that same year, she returned to children's literature with ‘Mago por casualidad’. In March, 2017, she published ‘Por una rosa’, a book that contains three stories written by three different novelists: Laura Gallego, Javier Ruescas and Benito Taibo; these are three stories set in the universe of the classic tale ‘Beauty and the Beast’. She has explored many of the literary subjects: she began with historical- fantasy literature with her story ‘Finis Mundi but science-fiction with her story ‘Las hijas de Tara’.

She wrote about epic fantasy. This type of literature was reflected in her story ’Memorias de Idhún’, she has written stories for children. In her fantasy narrative with ‘Memorias de Idhún’, the theme of love is just as or more important than the fantasy theme; the characters express their feelings, misgivings, etc. and are guided by them more so other concepts such as honour or duty. This is. Thus, reflection on one's own feeling occupies a lot of the space in the dialogues and the reproduction of thought; this fact is favoured by the decision to employ a passionate love triangle in his story ‘Memorias de Idhún’. She is inspired by some elements from the work of some novelists such as Margaret Weis and Tracy Hickman from their stories ‘La espada de Joram’, ‘Dragonlance’ and ‘El ciclo de la puerta de la muerte’, her books have been translated into a multitude of languages: Catalan, French, Danish, Norwegian, English, German, Portuguese and Chinese. 1999: Finis Mundi 2000: El Valle de los Lobos 2002: La maldición del Maestro 2003: La llamada de los muertos 2004: Fenris, el elfo 2004: Memorias de Idhún I: La Resistencia 2005: Memorias de Idhún II: Tríada 2006: Memorias de Idhún III: Panteón 2009: Sara y las goleadoras: Las chicas somos guerreras 2009: Sara y las goleadoras: Goleadoras en la liga 2010: Sara y las goleadoras: El fútbol y el amor son incompatibles 2010: Sara y las goleadoras: Las goleadoras no se rinden 2010: Sara y las goleadoras: El último gol 2001: El cartero de los sueños 2001: Retorno a la Isla Blanca 2002: Las hijas de Tara 2002: La leyenda del rey errante 2003: Mandrágora 2003: ¿Dónde está Alba?

2004: El coleccionista de relojes extraordinarios 2004: Alas de fuego 2004: La hija de la noche 2004: Max ya no hace reír 2004: Alba tiene una amiga muy especial 2005: El fantasma en apuros 2007: La emperatriz de los Etéreos 2008: Dos velas para el diablo 2009: Alas negras 2011: Dónde los árboles cantan 2012: Mago por casualidad 2013: El Libro de los Portales 2014: Enciclopedia de Idhún 2015: Todas las Hadas del Reino 2015: Héroes por casualidad 2016: Omnia: todo lo que puedas soñar 2017: Cuando me veas 2017: Por una rosa 2018: Guardianes de la Ciudadela: El bestiario de Axlin 2018: Guardianes de la Ciudadela: El secreto de Xein 2018: Guardianes