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
• 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.