Nonlinear convex programming

Nonlinear convex programming

1. Generalization of

   • Separable nonlinear programming
   • Nonlinear Quadratic Programming
   • g (x) is convex for all j
     • It guarantees to have an optimal local

2. Requires

   • F (x) when maximizing be concave and by minimizing convex
     • F(x) < 0
       • Nonlineal
   • Convex restrictions
     • G(x) > 0
     • Unrestricted or linear

3. Algorithms

   • Gradient
     • Get the solution to non-linear programming problems without restrictions
       • Estimation of the local minimum to a sequence of linear search problems
         • Search in each gradient, finding the iterative point
           • Minimum value of the function in the negative direction of the gradient
   • Non-directed sequential algorithms
     • Termination Function Method
       • It replaces an objective function with a barrier function and its parameter
     • Barrier Function Method
       • An objective function with a succession of penalty functions
     • They turn the original problem into a succession of unrestricted optimization problem
       • Their solutions converge to the solution of the original problem
       • Restrictions are added to the barrier function that is subtracted from the objective function
   • Sequential approach
     • Methods like
       • Linear approach
         • Frank-Wolfe
       • Quadratic approximation
         • Cuasi-Newton or Metric Variables
       • Replace the nonlinear objective function with a succession of linear or quadratic approximations
         • Sequence of feasible solutions
           • Converge to the optimal solution of the original problem

4. Aplicaciones

   • Factory production
     • Raw mixes
     • Costs and income
     • Available labor
   • Portfolio Optimization
   • Loss of energy
   • Network addressing
   • Design of electronic system parts