General lagrange-type functions in constrained global optimization Part I: auxiliary functions and optimality conditions

Abstract

The paper contains some new results and a survey of some known results related to auxiliary (Lagrange-type) functions in constrained optimization. We show that auxiliary functions can be constructed by means of two-step convolution of constraints and the objective function and present some conditions providing the validity of the zero duality gap property. We show that auxiliary functions are closely related to the so-called separation functions in the image space of the constrained problem under consideration. The second part of the paper (see Evtushenko et al., General Lagrange-type functions in constrained global optimization. Part 11: Exact Auxillary functions. Optimization Methods and Software) contains results related to exact auxiliary functions.

Keywords:

• Constrained optimization
• Auxiliary function
• Exact auxiliary function
• Separation function
• Convolution function
• Zero duality gap