79 research outputs found
Exact Solution Methods for the -item Quadratic Knapsack Problem
The purpose of this paper is to solve the 0-1 -item quadratic knapsack
problem , a problem of maximizing a quadratic function subject to two
linear constraints. We propose an exact method based on semidefinite
optimization. The semidefinite relaxation used in our approach includes simple
rank one constraints, which can be handled efficiently by interior point
methods. Furthermore, we strengthen the relaxation by polyhedral constraints
and obtain approximate solutions to this semidefinite problem by applying a
bundle method. We review other exact solution methods and compare all these
approaches by experimenting with instances of various sizes and densities.Comment: 12 page
Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması
Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized
Computing equilibria of Cournot oligopoly models with mixed-integer quantities
We consider Cournot oligopoly models in which some variables represent indivisible quantities. These models can be addressed by computing equilibria of Nash equilibrium problems in which the players solve mixed-integer nonlinear problems. In the literature there are no methods to compute equilibria of this type of Nash games. We propose a Jacobi-type method for computing solutions of Nash equilibrium problems with mixed-integer variables. This algorithm is a generalization of a recently proposed method for the solution of discrete so-called “2-groups partitionable” Nash equilibrium problems. We prove that our algorithm converges in a finite number of iterations to approximate equilibria under reasonable conditions. Moreover, we give conditions for the existence of approximate equilibria. Finally, we give numerical results to show the effectiveness of the proposed method
Using Column Generation to Solve Extensions to the Markowitz Model
We introduce a solution scheme for portfolio optimization problems with
cardinality constraints. Typical portfolio optimization problems are extensions
of the classical Markowitz mean-variance portfolio optimization model. We solve
such type of problems using a method similar to column generation. In this
scheme, the original problem is restricted to a subset of the assets resulting
in a master convex quadratic problem. Then the dual information of the master
problem is used in a sub-problem to propose more assets to consider. We also
consider other extensions to the Markowitz model to diversify the portfolio
selection within the given intervals for active weights.Comment: 16 pages, 3 figures, 2 tables, 1 pseudocod
Local Search Techniques for Constrained Portfolio Selection Problems
We consider the problem of selecting a portfolio of assets that provides the
investor a suitable balance of expected return and risk. With respect to the
seminal mean-variance model of Markowitz, we consider additional constraints on
the cardinality of the portfolio and on the quantity of individual shares. Such
constraints better capture the real-world trading system, but make the problem
more difficult to be solved with exact methods. We explore the use of local
search techniques, mainly tabu search, for the portfolio selection problem. We
compare and combine previous work on portfolio selection that makes use of the
local search approach and we propose new algorithms that combine different
neighborhood relations. In addition, we show how the use of randomization and
of a simple form of adaptiveness simplifies the setting of a large number of
critical parameters. Finally, we show how our techniques perform on public
benchmarks.Comment: 22 pages, 3 figure
Combining Alpha Streams with Costs
We discuss investment allocation to multiple alpha streams traded on the same
execution platform with internal crossing of trades and point out differences
with allocating investment when alpha streams are traded on separate execution
platforms with no crossing. First, in the latter case allocation weights are
non-negative, while in the former case they can be negative. Second, the
effects of both linear and nonlinear (impact) costs are different in these two
cases due to turnover reduction when the trades are crossed. Third, the
turnover reduction depends on the universe of traded alpha streams, so if some
alpha streams have zero allocations, turnover reduction needs to be recomputed,
hence an iterative procedure. We discuss an algorithm for finding allocation
weights with crossing and linear costs. We also discuss a simple approximation
when nonlinear costs are added, making the allocation problem tractable while
still capturing nonlinear portfolio capacity bound effects. We also define
"regression with costs" as a limit of optimization with costs, useful in
often-occurring cases with singular alpha covariance matrix.Comment: 21 pages; minor misprints corrected; to appear in The Journal of Ris
Hybridising local search with Branch-and-Bound for constrained portfolio selection problems
In this paper, we investigate a constrained portfolio selection problem with cardinality constraint, minimum size and position constraints, and non-convex transaction cost. A hybrid method named Local Search Branch-and-Bound (LS-B&B) which integrates local search with B&B is proposed based on the property of the problem, i.e. cardinality constraint. To eliminate the computational burden which is mainly due to the cardinality constraint, the corresponding set of binary variables is identified as core variables. Variable fixing (Bixby, Fenelon et al. 2000) is applied on the core variables, together with a local search, to generate a sequence of simplified sub-problems. The default B&B search then solves these restricted and simplified subproblems optimally due to their reduced size comparing to the original one. Due to the inherent similar structures in the sub-problems, the solution information is reused to evoke the repairing heuristics and thus accelerate the solving procedure of the subproblems in B&B. The tight upper bound identified at early stage of the search can discard more subproblems to speed up the LS-B&B search to the optimal solution to the original problem. Our study is performed on a set of portfolio selection problems with non-convex transaction costs and a number of trading constraints based on the extended mean-variance model. Computational experiments demonstrate the effectiveness of the algorithm by using less computational time
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