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    Linear Programming
    Go to Carnegie Mellon University
    Carnegie Mellon University

    Linear Programming

    Carnegie Mellon University

    Carnegie Mellon University

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    United States of America, Pittsburgh

    University RankQS Ranking
    58

    Key Facts

    Program Level

    PhD (Philosophy Doctorate)

    Study Type

    Full Time

    Delivery

    On Campus

    Application Fee

    USD 75 

    Campuses

    Main Site

    Program Language

    English

    Start & Deadlines

    Next Intake Deadlines22-Aug-2022
    Apply to this program

    Go to the official application for the university

    Duration 4 year(s)
    Tuition Fee
    USD 45,700  / year
    Next Intake 22-Aug-2022

    Linear Programming

    About

    Linear programming lies at the basis of modern optimization theory. This course focuses primarily on linear programming theory and algorithms, leaving beyond the scope of its practical applications. The main topics to be covered include modeling examples and expressive power of linear programs, polyhedral sets and their geometry, theory of systems of linear inequalities and duality, classical linear optimization algorithms (simplex and network simplex), and decomposition approaches for large-scale optimization. If time permits polynomial time solvability of linear programs, extensions to conic optimization problems, conic duality, and an introduction to interior point methods are topics of interest in the given order.

    Requirements

    Entry Requirements

    GPA

    3.41

    Average

    3.43

    Median

    3.03-3.76

    Middle 80%

    English Program Requirements

    Candidates are required to demonstrate a level of competence in English to meet the admissions requirements of the university. You are required to take a TOEFL, IELTS, or Duolingo exam unless:

    • You attended an undergraduate institution, earning a bachelor’s degree, where the sole language of instruction was English.
    • You earned a graduate degree where the sole language of instruction was English. (Although not required, we do recommend that you take the English Language Proficiency exam.)

    You must request that the official score be sent from the testing agency to our program for us to verify the score entered into the application. Request that the official score be sent to us using the following codes:

    • TOEFL Program Code: Institutional Code = 2074; Departmental Code = 02
      • Pro Tip: The recommended TOEFL score is 25 on each section of the Internet-based test. The minimum TOEFL scores required to apply for admission are: Reading: 20, Listening: 20, Speaking: 20, Writing: 20
    • IELTS Program Code: Select Carnegie Mellon and the Tepper School of Business 
      • Pro Tip: The recommended IELTS score is 7 overall and 7 in each band. The minimum IELTS scores required to apply for admission are: Listening: 7, Reading: 7, Writing: 7, Speaking: 7, Overall Band: 7
    • Duolingo Program Code: Select Carnegie Mellon University – Tepper School of Business
      • Pro Tip: The recommended Duolingo English Test (DET) score is 120 overall

    Pro Tip: TOEFL and IELTS scores are valid for two years and must be valid at the time you submit your application.

    Pro Tip: If you earned a degree from a non-U.S. institution, your academic documents should state that the sole language of instruction for the entire university was English in order to be eligible for a TOEFL/IELTS/Duolingo waiver. If your academic documents don’t include this, you should upload an official letter from the University Registrar indicating English as the mode of instruction for the entirety of the degree.

    Fee Information

    Tuition Fee

    USD 45,700 

    Application Fee

    USD 75 
    Carnegie Mellon University

    Linear Programming

    Carnegie Mellon University

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    United States of America,

    Pittsburgh

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