PhD in Modern Convex Optimization at Carnegie Mellon University

Carnegie Mellon University

United States of America, Pittsburgh

University Rank:#52

International students can study the Modern Convex Optimization at Carnegie Mellon University at its main campus in Pittsburgh , United States of America. This PhD degree is available as a Full Time program delivered on campus in English. The program has a duration of 4 years and is offered at the university's main campus. Students can apply for the next intake starting on August 22, 2027.

About PhD in Modern Convex Optimization

The purpose of this course is to give a solid foundation on convex optimization. Convex optimization, broadly speaking, is the most general class of optimization problems that are efficiently solvable. It has been fundamental in the development of Operations Research based decision making, and it naturally arises and is successfully used in a diverse set of applications in machine learning and high-dimensional statistics, signal processing, control, engineering, medical imaging, etc. In this course, we will focus on the modern aspects of convex optimization beyond Linear Programming, such as conic optimization including quadratic programming and semidefinite programming, and the main templates for efficient algorithms to solve large-scale convex optimization problems. It will concentrate on recognizing and solving convex optimization problems with an in-depth study of the underlying theory. The aim is to give students the background required to use these methods in their own research, and therefore our focus will be on the recent developments.

Requirements and Admission Criteria for PhD in Modern Convex Optimization at Carnegie Mellon University

Entry Requirements

GPA

3.41 Average

3.43 Median

3.03-3.76

Middle 80%

English Requirements

IELTSMin 7.5
TOEFLMin 102

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.

Tuition and Fee Information for PhD in Modern Convex Optimization at Carnegie Mellon University

Application Fee 75

PhD in Modern Convex Optimization at Carnegie Mellon University

Carnegie Mellon University

United States of America, Pittsburgh