scholarly journals A simulation test approach to the evaluation and comparison of unconstrained nonlinear optimization algorithms

1976 ◽  
Author(s):  
K. E. Hillstrom
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Algorithms ◽  
Simulation Test ◽  
Unconstrained Nonlinear Optimization

Fundamentals of Nonlinear Optimization

1995 ◽  
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Optimality Conditions ◽  
Nonlinear Optimization ◽  
Optimization Problems ◽  
Nonlinear Function ◽  
Nonlinear Least Squares ◽  
Sufficient Optimality Conditions ◽  
Science And Engineering ◽  
Chemical Phase ◽  
Unconstrained Nonlinear Optimization ◽  
Necessary And Sufficient

This chapter discusses the fundamentals of nonlinear optimization. Section 3.1 focuses on optimality conditions for unconstrained nonlinear optimization. Section 3.2 presents the first-order and second-order optimality conditions for constrained nonlinear optimization problems. This section presents the formulation and basic definitions of unconstrained nonlinear optimization along with the necessary, sufficient, and necessary and sufficient optimality conditions. An unconstrained nonlinear optimization problem deals with the search for a minimum of a nonlinear function f(x) of n real variables x = (x1, x2 , . . . , xn and is denoted as Each of the n nonlinear variables x1, x2 , . . . , xn are allowed to take any value from - ∞ to + ∞. Unconstrained nonlinear optimization problems arise in several science and engineering applications ranging from simultaneous solution of nonlinear equations (e.g., chemical phase equilibrium) to parameter estimation and identification problems (e.g., nonlinear least squares).

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