COURSE SUMMARY
Course Title:
Convex Optimization
Course Code:
19CCE333
Year Taught:
2019
Type:
Elective
Degree:
School:
School of Engineering
Campus:
Chennai
Coimbatore

Convex Optimization is an elective course offered in the B. Tech. in Computer and Communication Engineering program at School of Engineering, Amrita Vishwa Vidyapeetham.

Pre Requisite(s): Linear Algebra

### Objectives

• To efficiently solve mathematical optimization problems which arise in a variety of applications
• To discover/identify various applications in areas such as, estimation and signal processing, communications and networks, electronic circuit design, data analysis and modeling, statistics, automatic control systems and finance

### Course Outcomes

• CO1: Able to recognize, formulate, and analyze convex optimization problems
• CO2: Able to design sophisticated algorithms based on convex Optimization for applications in communication and signal processing
• CO3: Able to solve convex problems using computationally efficient techniques
• CO4: Able to analyze and evaluate optimization techniques

### CO – PO Mapping

 PO/PSO/CO PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12 PSO1 PSO2 CO1 3 3 3 3 - - - - - 3 - 3 3 3 CO2 3 3 3 3 3 - - - - 3 2 3 3 3 CO3 3 3 3 3 3 - - - - 3 2 3 3 3 CO4 - - - 3 3 - - - 2 3 2 3 3 3

#### SYLLABUS

Unit 1

Introduction - linear algebra fundamentals - Solving linear equations with factored matrices - Block elimination and Schur complements - Convex sets - Convex functions – examples.

Unit 2

Classes of Convex Problems - Linear optimization problems - Quadratic optimization problems - Geometric programming - Vector optimization -Reformulating a Problem in Convex Form.

Unit 3

Lagrange Duality Theory and KKT Optimality Conditions - Interior-point methods- Primal and Dual Decompositions – Applications.

#### TEXTBOOK / REFERENCE

Textbook(s)

• Stephen Boyd and LievenVandenberghe, “Convex Optimization”, Cambridge University Press, 2004.
• Daniel Palomar, “Convex Optimization in Signal Processing and Communications”, CambridgeUniversity Press, 2009.

Reference(s)

• Dimitri P Bertsekas, “Convex Optimization Theory”, Athena Scientific, 2009.

Evaluation Pattern

 Assessment Internal External Periodical 1 (P1) 15 - Periodical 2 (P2) 15 - *Continuous Assessment (CA) 20 - End Semester - 50 *CA – Can be Quizzes, Assignment, Projects, and Reports.