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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