American Institute of Mathematical Sciences

July  2012, 8(3): 733-747. doi: 10.3934/jimo.2012.8.733

A sequential convex program method to DC program with joint chance constraints

 1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China, China 2 School of Sciences, Dalian Ocean University, Dalian 116023, China 3 School of Computer Science and Technology, Dalian University of Technology, Dalian 116023, China

Received  September 2011 Revised  March 2012 Published  June 2012

In this paper, we consider a DC (difference of convex) programming problem with joint chance constraints (JCCDCP). We propose a DC function to approximate the constrained function and a corresponding DC program ($\textrm{P}_{\varepsilon}$) to approximate the JCCDCP. Under some mild assumptions, we show that the solution of Problem ($\textrm{P}_{\varepsilon}$) converges to the solution of JCCDCP when $\varepsilon\downarrow 0$. A sequential convex program method is constructed to solve the Problem ($\textrm{P}_{\varepsilon}$). At each iteration a convex program is solved based on the Monte Carlo method, and the generated optimal sequence is proved to converge to the stationary point of Problem ($\textrm{P}_{\varepsilon}$).
Citation: Xiantao Xiao, Jian Gu, Liwei Zhang, Shaowu Zhang. A sequential convex program method to DC program with joint chance constraints. Journal of Industrial & Management Optimization, 2012, 8 (3) : 733-747. doi: 10.3934/jimo.2012.8.733
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