An Outer Approximation Algorithm Guaranteeing Feasibility of Solutions and Approximate Accuracy of Optimality

  • Authors:

  • Syuuji Yamada;Tamaki Tanaka

  • Affiliations:

  • Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, Osaka 565-0871, Japan;Department of Mathematical System Science, Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan (E- mail: tanaka@si.hirosaki-u.ac.jp)

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 1999

Quantified Score

Hi-index 0.00

Visualization

Abstract

We treat a concave programming problem with a compact convex feasible set. Assuming the differentiability of the convex functions which define the feasible set, we propose two solution methods. Those methods utilize the convexity of the feasible set and the property of the normal cone to the feasible set at each point over the boundary. Based on the proposed two methods, we propose a solution algorithm. This algorithm takes advantages over classical methods: (1) the obtained approximate solution is always feasible, (2) the error of such approximate value can be evaluated properly for the optimal value of such problem, (3) the algorithm does not have any redundant iterations.