Related papers: Sparse High-Order Portfolios via Proximal DCA and …
The Mean-Variance-Skewness-Kurtosis (MVSK) portfolio optimization model is a quartic nonconvex polynomial minimization problem over a polytope, which can be formulated as a Difference-of-Convex (DC) program. In this manuscript, we…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing…
The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of…
We consider the multi-objective mean-variance-skewness-kurtosis (MVSK) problem in portfolio selection, with and without shorting and leverage. Additionally, we define a sparse variant of MVSK where feasible portfolios have supports…
Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…
We extend the classical mean-variance (MV) framework and propose a robust and sparse portfolio selection model incorporating an ellipsoidal uncertainty set to reduce the impact of estimation errors and fixed transaction costs to penalize…
We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…
This paper introduces a novel penalty decomposition algorithm customized for addressing the non-differentiable and nonconvex problem of extended mean-variance-CVaR portfolio optimization with short-selling and cardinality constraints. The…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC…
In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The…
In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue…
We study a cardinality-constrained optimization problem with nonnegative variables in this paper. This problem is often encountered in practice. Firstly we study some properties on the optimal solutions of this optimization problem under…
One of the reasons that higher order moment portfolio optimization methods are not fully used by practitioners in investment decisions is the complexity that these higher moments create by making the optimization problem nonconvex. Many few…
We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…
We consider stochastic optimization problems with non-convex functional constraints, such as those arising in trajectory generation, sparse approximation, and robust classification. To this end, we put forth a recursive momentum-based…
In this paper, we propose a single-loop stochastic gradient algorithm for solving stochastic nonconvex-concave minimax optimization with nonlinear convex coupled constraints (MCC). The proposed method, SPACO (Stochastic Penalty-based…
Mean-reverting portfolios with volatility and sparsity constraints are of prime interest to practitioners in finance since they are both profitable and well-diversified, while also managing risk and minimizing transaction costs. Three main…
We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global…