This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very “varied” class of problems, comprising sub-classes of problems ranging from trivial to undecidable. Solution methods for QP are very diverse, ranging from entirely co...

The seller of a contingent claim H can always find a self-financing investment strategy that (super)hedges the claim H. When the seller wants to endow an initial capital x less than the one required to get perfect (super)hedging, the shortfall risk minimisation problem arises in a natural way. The aim is to find the strategy that minimises E{`([H(ST )−V x,φ T ])} (shortfall risk), where V x,φ t...

We derive multiplicative updates for solving the nonnegative quadratic programming problem in support vector machines (SVMs). The updates have a simple closed form, and we prove that they converge monotonically to the solution of the maximum margin hyperplane. The updates optimize the traditionally proposed objective function for SVMs. They do not involve any heuristics such as choosing a learn...

This paper studies the Discrete-Time Switched LQR problem over an infinite time horizon, subject to polyhedral constraints on state and control inputs. Specifically, we aim to find an infinite-horizon hybrid-control sequence, i.e., a sequence of continuous and discrete (switching) control inputs, that minimizes an infinite-horizon quadratic cost function, subject to polyhedral constraints on st...

When recording data, large errors may occur occasionally. The corresponding abnormal data points, called outliers, can have drastic effects on the estimates. There are several ways to cope with outliers 0 detect and delete or adjust the erroneous data, use a modified cost function. We propose a new approach that allows, by introducing additional variables, to model the outliers and to detect th...

ε-support vector regression (ε-SVR) can be converted into an unconstrained convex and non-smooth quadratic programming problem. It is not solved by the traditional algorithm. In order to solve this non-smooth problem, a class of piecewise smooth functions is introduced to approximate the ε-insensitive loss function of ε-SVR, which generates a ε-piecewise smooth support vector regression (ε-dPWS...

In this paper a regularized stochastic decomposition algorithm with master programs of finite size is described for solving two-stage stochastic linear programming problems with recourse. In a deterministic setting cut dropping schemes in decomposition based algorithms have been used routinely. However, when only estimates of the objective function are available such schemes can only be properl...

The decomposition method is currently one of the major methods for solving the convex quadratic optimization problems being associated with support vector machines. For a special case of such problems the convergence of the decomposition method to an optimal solution has been proven based on a working set selection via the gradient of the objective function. In this paper we will show that a ge...

The problem of selecting a portfolio has been largely faced in terms of minimizing the risk, given the return. While the complexity of the quadratic programming model due to Markowitz has been overcome by the recent progress in algorithmic research, the introduction of linear risk functions has given rise to the interest in solving portfolio selection problems with real constraints. In this pap...

Recently, Liu and Wang described an interesting numerical method to a special class of interval quadratic programming, where the linear term in objective function and constraints involving interval coefficients (Appl. Math. Comput. (2007), doi:10.1016/j.amc.2006.12.007). In this paper, we generalize Liu and Wang’s method to general interval quadratic programming, where all coefficients in the o...