2018/03/19 by B. Muraleetharan, Muraleetharan, B., Shitharth Selvarajan +5
Computer Science · Mathematics · #41A29 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1804.02270
openalex publication_date 2018/03/19 · openalex created_date 2018/04/13 · openalex updated_date 2026/07/28
In this paper we consider three minimization problems, namely quadratic, ρ-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and discrete mixed variables. The ρ-convex problem is considered with ρ-convex inequality constraints in mixed variables. The quadratic fractional problem is studied with quadratic fractional constraints in mixed variables. For all three problems we reformulate the problem as a mathematical programming problem and apply standard Karush Kuhn Tucker necessary conditions. Then, for each problem, we provide local necessary optimality condition. Further, for each problem a Lagrangian multiplier sufficient optimality condition is provided to identify global minimizer among the local minimizers. For the quadratic problem underestimation of a Lagrangian was employed to obtain the desired sufficient conditions. For the ρ-convex problem we obtain two sufficient optimality conditions to distinguish a global minimizer among the local minimizers, one with an underestimation of a Lagrangian and the other with a different technique. A global sufficient optimality condition for the quadratic fractional problem is obtained by reformulating the problem as a quadratic problem and then utilizing the results of the quadratic problem. Examples are provided to illustrate the significance of the results obtained.