**(S) = Spring and (F) = Fall**

**CAAM 378 (F) INTRODUCTION TO OPERATIONS RESEARCH AND OPTIMIZATION**

Formulation and solution of mathematical models in management, economics, engineering and science applications in which one seeks to minimize or maximize an objective function subject to constraints including models in linear, nonlinear and integer programming; basic solution methods for these optimization models; problem solving using a modeling language and optimization software.

*Recommended Prerequisite(s)*: MATH 212 and any one of the following: CAAM 335, MATH 211, or MATH 355.

**CAAM 454 (S) NUMERICAL ANALYSIS II**

Iterative methods for linear systems of equations including Krylov subspace methods; Newton and Newton-like methods for nonlinear systems of equations; Gradient and Newton-like methods for unconstrained optimization and nonlinear least squares problems; techniques for improving the global convergence of these algorithms; linear programming
duality and primal-dual interior-point methods.
Credit may not be received for both CAAM 454 and CAAM 554.

*Recommended Prerequisite(s)*: CAAM 453.

**CAAM 471 (S) INTRODUCTION TO LINEAR AND INTEGER PROGRAMMING**

Linear and integer programming involve formulating and solving fundamental optimization models widely used in practice. This course introduces the basic theory, algorithms, and software of linear and integer programming. Topics studied in the linear programming part include polyhedron concepts, simplex methods, duality, sensitivity analysis and decomposition techniques. Building on linear programming, the second part of this course introduces modeling with integer variables and solution methodologies in integer programming including branch-and-bound and cutting-plane techniques. This course will provide a basis for further studies in convex and combinatorial optimization.

*Recommended Prerequisite(s)*: CAAM 335.

**CAAM 474 (F) COMBINATORIAL OPTIMIZATION**

General theory and approaches for solving combinatorial optimization problems are studied. Specific topics include basic polyhedral theory, minimum spanning tress, shortest paths, network flow, matching and matroids. The course also cover the traveling salesman problem.

*Recommended Prerequisite(s)*: CAAM 378 or 471.

__Biennial; Offered in Even Years__

**CAAM 554 (S) NUMERICAL ANALYSIS II**

This course covers the same lecture material as CAAM 454, but fosters greater theoretical sophistication through more challenging problem sets and exams.
Credit may not be received for both CAAM 454 and CAAM 554.

*Recommended Prerequisite(s)*: CAAM 553.

**CAAM 560 (F) OPTIMIZATION THEORY**

Derivation and application of necessity conditions and sufficiency conditions for constrained optimization problems.

**CAAM 564 (S) NUMERICAL OPTIMIZATION**

Numerical algorithms for constrained optimization problems in engineering and sciences, including simplex and interior-point methods for linear programming, penalty, barrier, augmented Lagrangian and SQP methods for nonlinear programming.

*Recommended Prerequisite(s)*: CAAM 560 (may be taken concurrently) and CAAM 454.

__Biennial; Offered in Even Years__

**CAAM 565 (F) CONVEX OPTIMIZATION**

Convex optimization problems arise in communication, system theory, VLSI, CAD, finance, inventory, network optimization, computer vision, learning, statistics, ... etc, even though oftentimes convexity may be hidden and unrecognized. Recent advances in interior-point methodology have made it much easier to solve these problems and various solvers are now available. This course will introduce the basic theory and algorithms for convex optimization, as well as its many applications to computer science, engineering, management science and statistics.

*Recommended Prerequisite(s)*: CAAM 335 and CAAM 401

__Biennial; Offered in Odd Years__

**CAAM 571 (S) INTRODUCTION TO LINEAR AND INTEGER PROGRAMMING**

This course covers the same lecture material as CAAM 471, but fosters greater theoretical sophistication through more challenging problem sets and exams. Credit may not be received for both CAAM 471 and CAAM 571.

**CAAM 640 (BOTH) OPTIMIZATION WITH SIMULATION CONSTRAINTS**

Content varies from year to year. Course may be repeated for credit.

*Recommended Prerequisite(s)*: CAAM 564.

**CAAM 654 (BOTH) TOPICS IN OPTIMIZATION**

Content varies from year to year.