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The portfolio optimization theory has arisen from the age of a twin criterion, which is composed of risk and return, taking into account the complexity of investors’ qualities together with their preferences and an overwhelming range of financial goods. The goal of the portfolio optimization issue is to determine, given the size or securities of the assets, the optimal solution for an investment in a portfolio as a specified value. The portfolio optimization mathematical problem can be formulated in a variety of ways. The significant modes to represent this problem are outlined below:

i. Estimate the minimum value of the risk for a stipulated value of the expected return

ii. Estimate the maximum value of the expected return for a given value of the risk

iii. Estimate the minimum value of the risk and maximum value of expected return based on a specified value of a coefficient representing risk aversion level

iv. Estimate the minimum value of the risk irrespective of the value of the expected return

v. Estimate the maximum value of expected return irrespective of the value of the risk