Geometric compromise programming: application in portfolio selection

Compromise programming (CP) aims to find solutions by minimising distances an ideal point with maximum achievement which is usually infeasible. A common assumption in CP that it highly unlikely the optimum decision will lie out of bounds compromise set given metrics p = 1 $p=1$ and ∞ $p=\infty$ Minkowski distance function. This excludes use multiplicative functions as a measure achievement. We propose geometric (GCP) provide alternative based on overcome this limitation. methodology extension allows incorporate principle limited compensability. An additional interesting feature GCP that, under reasonable assumptions, characterises extreme seekers' behaviour non-concave utility (expressing no preference for any extremes). discuss practical implications our approach present three numerical illustrations context portfolio selection.