The exhaustive list of topics in Optimization Methods in which we provide **Help with Homework Assignment** and **Help with Project** is as follows:

**Concept:**- Historical Development
- Engineering applications of Optimization
- Art of Modeling Objective function
- Constraints and Constraint surface
- Formulation of design problems as mathematical programming problems
- Classification of optimization problems
- Optimization techniques – classical and advanced techniques.

**Optimization using Calculus:**- Stationary points
- Functions of single and two variables
- Global Optimum.
- Convexity and concavity of functions of one and two variables.
- Optimization of function of one variable and multiple variables
- Gradient vectors.
- Optimization of function of multiple variables subject to equality constraints
- Lagrangian function.
- Optimization of function of multiple variables subject to equality constraints
- Hessian matrix formulation
- Eigen values.
- Kuhn-Tucker Conditions

**Linear Programming:**- Standard form of linear programming (LP) problem
- Canonical form of LP problem
- Assumptions in LP Models
- Elementary operations.
- Graphical method for two variable optimization problem.
- Motivation of simplex method
- Simplex algorithm and construction of simplex table
- Simplex criterion
- Minimization versus maximization problems.
- Revised simplex method
- Duality in LP
- Primal-dual relations
- Dual Simplex method
- Sensitivity or post optimality analysis.
- Other algorithms for solving LP problems
- Karmarkar’s projective scaling method.

**Linear Programming Applications**- Use of software for solving linear optimization problems using graphical and simplex methods.
- Transportation
- Assignment
- Water resources
- Structural and other optimization problems.

**Dynamic Programming:**- Sequential optimization
- Representation of multistage decision process
- Types of multistage decision problems
- Concept of sub optimization and the principle of optimality.
- Recursive equations – Forward and backward recursions
- Computational procedure in dynamic programming (DP).
- Discrete versus continuous dynamic programming
- Multiple state variables
- Curse of dimensionality in DP.

**Dynamic Programming Applications:**- Problem formulation and application in Design of continuous beam and Optimal geometric layout of a truss.
- Water allocation as a sequential process.
- Capacity expansion and Reservoir operation.

**Integer Programming:**- Integer linear programming
- Concept of cutting plane method.
- Mixed integer programming
- Solution algorithms.

**Advanced Topics in Optimization**- Piecewise linear approximation of a nonlinear function.
- Multi objective optimization – Weighted and constrained methods
- Multi level optimization.
- Direct and indirect search methods.
- Evolutionary algorithms for optimization and search
- Applications in civil engineering