## Contributed Session Fri.2.H 1029

#### Friday, 13:15 - 14:45 h, Room: H 1029

**Cluster 15: Multi-objective optimization** [...]

### Portfolio selection

**Chair: Carlos Abad**

**Friday, 13:15 - 13:40 h, Room: H 1029, Talk 1**

**Carlos Abad**

Portfolio selection with multiple spectral risk constraints

**Coauthor: Garud Iyengar**

**Abstract:**

We propose an iterative algorithm to efficiently solve the portfolio

selection with multiple spectral risk constraints. Since the conditional

value at risk~(CVaR) is a special case of the spectral risk function, our

algorithm solves portfolio selection problems with multiple CVaR

constraints. In each step, the

algorithm solves a very simple separable convex quadratic program. The

algorithm extends to the case where the objective is a

utility function with mean return and a weighted combination of

a set of spectral risk constraints, or maximum of a set of spectral risk

functions. We report numerical results that show that our proposed

algorithm is very efficient, and is at least two orders of magnitude

faster than the state of the art general purpose solver for all practical

instances.

**Friday, 13:45 - 14:10 h, Room: H 1029, Talk 2**

**Mohammad Ali Yaghoobi**

Using ball center of a polytope to solve a multiobjective linear programming problem

**Coauthor: Alireza H. Dehmiry**

**Abstract:**

Recently, ball center of a polytope as the center of a largest ball inside the polytope is applied to solve a single objective linear programming problem. The current research aims to develop an algorithm for solving a multiobjective linear programming problem based on approximating ball center of some polytopes obtained from the feasible region. In fact, the proposed algorithm asks a weight vector from the decision maker and then tries to solve the problem iteratively. It is proved that the algorithm converges to an epsilon efficient solution after a finite number of iterations. Moreover, the well performance of it in comparison with the well known weighted sum method is discussed. Furthermore, numerical examples and a simulation study are used to illustrate the validity and strengths of the recommended algorithm.