QP is the optimization of a quadratic function subject to linear equality and inequality constraints. It arises in multiple objective decision making where the departure of the actual decisions from their corresponding ideal, or bliss, value can be evaluated using a weighted quadratic norm as a measure of deviation. The formulation of mean-variance optimization of uncertain systems also leads t...

Portfolio optimization involves the optimal assignment of limited capital to different available financial assets to achieve a reasonable trade-off between profit and risk objectives. In this paper, we studied the extended Markowitz’s meanvariance portfolio optimization model. We considered the cardinality, quantity, pre-assignment and round lot constraints in the extended model. These four rea...

Given a combinatorial optimization problem Π and an increasing finite sequence c of natural numbers, we obtain a cardinality constrained version Πc of Π by permitting only those feasible solutions of Π whose cardinalities are members of c. We are interested in polyhedra associated with those problems, in particular in inequalities that cut off solutions of forbidden cardinality. Maurras [11] an...

In this paper we consider cardinality-constrained convex programs that minimize a convex function subject to a cardinality constraint and other linear constraints. This class of problems has found many applications, including portfolio selection, subset selection and compressed sensing. We propose a successive convex approximation method for this class of problems in which the cardinality funct...

We determine the optimal dynamic investment policy for a mean quadratic variation objective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). We compare the efficient frontiers and optimal investment policies for three mean variance like strategies: pre-commitment mean variance, time-consistent mean variance, and mean quadratic vari...

Optimization problems with cardinality constraints are very difficult mathematical programs which are typically solved by global techniques from discrete optimization. Here we introduce a mixed-integer formulation whose standard relaxation still has the same solutions (in the sense of global minima) as the underlying cardinality-constrained problem; the relation between the local minima is also...

The paper concerns optimal mean-variance proportional reinsurance under group correlation. In order to solve the corresponding constrained quadratic optimization problem, we make large recourse both to the smart friendly technique originally proposed by B. de Finetti in his pioneering paper and to the well known Karush-Kuhn-Tucker conditions for constrained optimization. We offer closed form re...

Human cytomegalovirus (HCMV) strains may be genotyped based on polymorphisms that exist within the UL144 gene, which is one of 19 viral genes lost in attenuated laboratory strains. In the present study, UL144 genotypes in congenitally infected babies (congenital cytomegalovirus [cCMV]) were determined, and the relationship between the genotype, viral load, cytokine profile, and patient developm...

5 We determine the optimal dynamic investment policy for a mean quadratic variation ob6 jective function by numerical solution of a nonlinear Hamilton-Jacobi-Bellman (HJB) partial 7 differential equation (PDE). We compare the efficient frontiers and optimal investment poli8 cies for three mean variance like strategies: pre-commitment mean variance, time-consistent 9 mean variance, and mean quad...