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为了研究能使风险最小、收益最大的最优组合投资问题，首先建立了多目标规划模型，并利用约束法将该多目标规划问题转化为单目标规划问题．用单纯形法求解，得出在给定风险损失率下的最大收益率，并根据这些数据拟会风险收益曲线（该问题的有效解集的有效边界）．为了寻求最优组合投资方案，给出一种确定无差异曲线的方法，该无差异曲线能体现投资者决策准则．无差异曲线与风险收益曲线的公切点所对应的组合投资方案即为所寻求的最优组合投资方案．
In order to study the optimal portfolio investment which can minimize the risk and maximize the profit, a multi-objective programming model is first established and the multi-objective programming problem is transformed into a single-objective programming problem by using the constraint method. Using the simplex method to solve, we get the maximum rate of return for a given risk loss rate, and based on these data, we get the risk return curve (the effective boundary of the effective solution set of the problem). In order to find the optimal portfolio investment scheme, a method to determine the indifference curve is given. The indifference curve can reflect the investor decision criteria. The portfolio investment scheme corresponding to the common cutoff point of the indifference curve and the risk-return curve is the optimal portfolio investment solution sought.