Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Relaxed Optimization Approach for Cardinality-Constrained Portfolio
  Optimization   A cardinality-constrained portfolio caps the number of stocks to be traded
across and within groups or sectors. These limitations arise from real-world
scenarios faced by fund managers, who are constrained by transaction costs and
client preferences as they seek to maximize return and limit risk.
  We develop a new approach to solve cardinality-constrained portfolio
optimization problems, extending both Markowitz and conditional value at risk
(CVaR) optimization models with cardinality constraints. We derive a continuous
relaxation method for the NP-hard objective, which allows for very efficient
algorithms with standard convergence guarantees for nonconvex problems. For
smaller cases, where brute force search is feasible to compute the globally
optimal cardinality- constrained portfolio, the new approach finds the best
portfolio for the cardinality-constrained Markowitz model and a very good local
minimum for the cardinality-constrained CVaR model. For higher dimensions,
where brute-force search is prohibitively expensive, we find feasible
portfolios that are nearly as efficient as their non-cardinality constrained
counterparts.

20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph