Course Schedule - Spring 2026

Date	Day	Topic	Book Chapter	Class Page	Other
1/12	M	Mathematical Preliminaries: The space \(\mathbb{R}^n\), Inner products, Vector norms, Cauchy Schwarz inequality	1	1-1
1/14	W	Mathematical Preliminaries: Matrix operations, Symmetric matrices, Definite matrix, Orthogonal matrix, Matrix norms, Eigenvalues & Eigenvectors	1	1-2
1/16	F	Mathematical Preliminaries: Topological concepts; Differentiability - Jacobian, Hessian, directional derivative	1	1-3
1/19	M	No class - University Holiday
1/21	W	Optimality conditions: Global optima, argmin and argmax, infima and suprema, extreme value theorem (EVT), generalized EVT for metric spaces, stationary points, first order optimality condition	2.1	2-1	Quiz 1
1/23	F	Optimality conditions: Eigvals of definite matrices, Second order optimality conditions	2.2, 2.3	2-2
1/26	M	Optimality conditions: Coercive functions, Quadratic functions, Convex functions, Global optimality	2.4, 2.5	2-3
1/28	W	Least squares: Ordinary Least squares (OLS), Linear Data fitting, Polynomial fitting	3.1, 3.2	3-1
1/30	F	Least squares: Regularized least squares, Tikhonov regularization, De-noising	3.3, 3.4	3-2	HW 1 Due
2/2	M	Gradient method: Descent direction, Gradient descent algorithm	4.1, 4.2	4-1
2/4	W	Gradient method: Condition number, Gradient descent solution sensitivity, Diagonal scaling	4.3, 4.4,	4-2	Quiz 2
2/6	F	Gradient method: Lipschitz continuity, Convergence of the gradient method	4.7	4-3
2/9	M	Mathematical Preliminaries: Linear approximation theorem, Quadratic approximation theorem Newton’s method: Pure Newton’s method, Newton method quadratic local convergence	5.1	5-1
2/11	W	Mathematical Preliminaries: Cholesky factorization Newton’s method: Damped Newton’s method, Hybrid gradient-Newton method	5.2, 5.3	5-2	HW 2 Due Th Feb 12
2/13	F	No Classes (Rememberance Day)
2/16	M	Midterm 1 review (bring questions!)
2/18	W	Midterm 1
2/20	F	Convex set: Definition, Algebraic operations on convex sets, Topological Properties of Convex Sets, Convex hull	6.1, 6.2, 6.3, 6.5	6-1
2/23	M	Convex set: Convex cones, Conic combinations	6.4	6-2
2/25	W	Convex set: Convex polytope, Feasible region, Basic feasible solutions, Extreme points	6.6	6-3	Quiz 3
2/27	F	Convex function: Definition, First and Second order characterization, Operations preserving convexity	7.1, 7.2, 7.3, 7.4	7-1
3/2 - 3/6	MWF	Spring Break - No Class
3/9	M	Convex function: Sublevel sets of convex functions (vid), Continuity and differentiability of convex functions (vid), Extended real-valued functions (vid), Maxima of a convex function (vid)	7	WS18
3/11	W	Convex function: Review Chapters 6 & 7 content in preparation for this lecture	7	WS19
3/13	F	Convex optimization problems: Definition (vid), Linear programming (vid), Convex quadratic problems (vid), Chebyshev center for a set of points (vid)	8	WS20	HW 3 Due
3/16	M	Convex optimization problems: The orthogonal projection operator: intro (vid), Projection on the non-negative orthant (vid), Projection on B[0,r] (vid, and will cover in class)	8	WS21
3/18	W	Convex optimization problems: Review Chapters 6, 7 and 8 in preparation for this lecture	8	WS22	Quiz 4
3/20	F	Optimization over a convex set: Stationarity (vid), Stationarity in convex problems (vid), Orthogonal projection revisited (vid), Gradient projection method (vid)	9	WS23	HW 4 Due
3/23	M	Review	9	WS24/25/26
3/25	W	Midterm 2
3/27	F	Optimality conditions: Motivation (vid), Separation and alternative theorems (vid), KKT conditions (vid), Lagrangian function (vid, plus in-class), Example (in-class)	10	WS27
3/30	M	Optimality conditions: Orthogonal projection onto an affine space (vid), Orthogonal projection onto hyperplanes (vid), Orthogonal regression (vid)	10	WS28
4/1	W	Optimality conditions: Ch 10 Practice problems. Please review Ch 10 content before this class.	10	WS29	Quiz 5
4/3	F	Optimality conditions: Active constraints (vid) KKT conditions: Feasible descent direction (vid), Inequality and equality constrained problems (vid), Example: Equality constrained (vid), Example KKT not satisfied (vid)	Chapters 10-11	WS30
4/6	M	KKT conditions: The convex case: KKT sufficiency (vid), Slater conditions (vid), The convex case: KKT necessity (vid), Example1: planning the solution (in-class), Example2: planning the solution (in-class)	11	WS31
4/8	W	KKT conditions: Ch11 Practice problems. Please review Ch11 content before this class.	11	WS32
4/10	F	Duality: Motivation (vid), Definition and weak duality (vid), Weak duality: tight bound example (vid), Weak duality: poor bound example (vid), Strong duality in the convex case (vid)	12	WS33	HW 5 Due
4/13	M	Duality: Possibly different ways to construct the dual (in-class), Dual for linear programming (vid), Dual for strictly convex quadratic programming (vid)	12	WS34
4/15	W	Duality: Dual for convex quadratic programming (vid)	12	WS35	Quiz 6
4/17	F	Duality: Install CVXPY on your Python environment, Read about Disciplined Convex Programming (DCP), Read What is CVXPY page including the Constraints section	12	WS36	HW 6 Due
4/20	M	Midterm 3 review (bring questions!)		WS37
4/22	W	Midterm 3
4/23	F	No class (EGR Design Day)