Goal Driven Optimization

Melvyn Sim (dscsimmnus.edu.sg)
Wenqing Chen (chenwenqinggmail.com)

Abstract: Achieving a targeted objective, goal or aspiration level are relevant aspects of decision making under uncertainties. We develop a goal driven stochastic optimization model that takes into account an aspiration level. Our model maximizes the shortfall aspiration level criterion}, which encompasses the probability of success in achieving the goal and an expected level of under-performance or shortfall. The key advantage of the proposed model is its tractability. We show that proposed model is reduced to solving a small collections of stochastic linear optimization problems with objectives evaluated under the popular conditional-value-at-risk (CVaR) measure. Using techniques in robust optimization, we propose a decision rule based deterministic approximation of the goal driven optimization problem by solving a polynomial number of second order cone optimization problems (SOCP) with respect to the desired accuracy. We compare the numerical performance of the deterministic approximation with sampling approximation and report the computational insights.

Keywords: aspiration level, risk, robust optimization, maximizing probability

Category 1: Robust Optimization

Category 2: Stochastic Programming

Citation: Working paper, NUS Business School

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Entry Submitted: 05/26/2006
Entry Accepted: 05/26/2006
Entry Last Modified: 05/26/2006

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