A Lagrange duality approach for multi-composed optimization problems

作者：Wanka Gert^*; Wilfer Oleg

来源：Top, 2017, 25(2): 288-313.

DOI：10.1007/s11750-016-0431-2

• Lagrange duality
• Composed functions
• Generalized interior point regularity conditions
• Conjugate functions
• Reciprocals of concave functions
• Power functions

In this paper, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of functions. For this problem, we calculate its conjugate dual problem, where the functions involved in the objective function of the primal problem will be decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach, we determine the formulas of the conjugate as well as the biconjugate of the objective function of the primal problem and discuss an optimization problem having as objective function the sum of reciprocals of concave functions.

• 出版日期2017-7