Schedule and Notes
Week  Dates Topics  Notes  Assignments 
1 
Jan. 4:
Panorama of optimization problems; scope of the course. 
Lecture 2 
Homework 1 
2 
Jan. 9:
Unconstrained minimization in finite number of variables: necessary and sufficient conditions
Constrained minimization with equality constraints: Lagrange multiplier concept Necessary conditions for constrained minimization (two variables). Jan. 11: Necessary conditions for constrained minimization (N variables). 

Homework 2 
3 
Jan. 16:
Sufficient conditions for constrained minimization; Bordered Hessian
Genesis of calculus of variations Calculus of variations problems in geometry and mechanics Jan. 18: Calculus of variations problems in geometry and mechanics (contd.) Formulating calculus of variations problems. 
obj.m (Objective function file) g1.m (Nonlinear constraints file) Lecture 4 Lecture 5, Lecture 6 
 
4 
Jan. 23:
Mathematical preliminaries to calculus of variations: vector spaces and their properties; function spaces
Jan. 25: Mathematical preliminaries to calculus of variations (contd.): Gateaux variation 
Lecture 8 
Homework 3 
5 
Jan. 30:
Frechet differential, Frechet derivative EulerLagrange equations; How did Lagrange derive them? fundamental lemma of calculus of variations EulerLagrange equations; How did Lagrange derive them? How did Euler derive them? Variational derivative Feb. 1: Extension of EulerLagrange equations to multiple derivatives; beam problem 
Lecture 10 Lecture 11 
Homework #4 
6 
Feb. 6:
Extension of EulerLagrange equations to multiple derivatives and multiple functions EulerLagrnage equations when there are two independent variables of the unknown function. Feb. 8: EulerLagrange equations when there are three independent variables of the unknown function. 

 
7 
Feb. 13:
Happy jagaran! (Holiday for Mahasivarathri)
Feb. 15: Global (functional type) constraints in variational calculus Local (pointwise or function type) constraints in variational calculus 
Lecture 14 
Homework 5 
8 
Feb. 20:
Variable end conditions in calculus of variations; WeierstrassErdmann corner conditions; broken extremails.
Feb. 22: First integrals of EulerLagrange equations; change of variables; parametric form; transformation with a parameter and Noether's theorm. 
Lecture 16 
Homework 6 
9 
Feb. 27:
"Inverse" EulerLagrange equations problem: going from the differential equation to the functional to be optimized: three methods, (i) for selfadjoint operators, (ii) integrating factor method for dissipative systems, and (iii) parallel generative system for dissipative cases.
Mar. 1: Practice problems in calculus of variations 
Lecture 18: Some problems in calculus of variations 
 
10 
Mar 6:
Midterm examination during the classtime: 8:30 AM to 10:30 AM.
Mar 8: Glimpses of structural optimization 
Lecture 18: Solutions to midterm 2017 
Midterm examination 
11 
Mar 13:
Optimization of crosssection area of an axially loaded bar; multiple formulations involving volume,
strain energy, potential energy, displacement, and stress.
Mar 15: Optimality criteria method implemented for an axially loaded bar. 
Lecture 19b: Solutions to Problems 1 and 8 Download Matlab files of bar optimization problems solved using the optimality criteria method 
Homework #7

12 
Mar 20:
Optimization of crosssection area of a beam in multiple settings.
Mar 22: Optimality criteria method implemented for a beam. 
Download Matlab files of beam optimization problem solved using the optimality criteria method 
 
13 
Mar. 27:
Optimization of a truss and its implementation in Matlab.
Sensitivity analysis and optimality criterion; adjoint method Mar. 29: Holiday for Mahaveer Jayanthi 
Truss FEA files 
Homework 8 
14 
Apr. 3:
Free vibration problem as a calculus of variations problem
Apr. 5: Minimization characterization of SturmLiouville problems Strongest column: optimization for buckling load. 
Minimum characterization of structural optimization problems 
 
15 
Apr. 10:
Optimization for transient problems.
Apr. 12: Structural optimization in multiphysics problems 
A short discussion on Electrothermalelastic structure optimization 
 
16 
Apr. 18:
Final examination at 2:00 PM to 3:30 PM in the ME MMCR on April 18, 2018. It will be followed by two project presentations.
April 30: Project presentations on April 30, 2018, starting at 8:30 AM in ME MMCR. Each project gets 15 min (including Q&A time of 2 min). 

Project presentation; pdf file of the PPT file to be submitted soon after the presentation by email. 
You can find the contentpage of the previous years here.
2017
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2015
2014
2013
2012
2011
2009
2007
2006
2005