We introduce disciplined convex stochastic programming (DCSP), a modeling framework that can significantly lower the barrier for modelers to specify and solve convex stochastic optimization problems, by allowing modelers to naturally express a wide variety of convex stochastic programs in a manner that reflects their underlying mathematical representation. DCSP allows modelers to express expect...

A one{to{one relation is established between the nonnegative spectral values of a vector in a primitive symmetric cone and the eigenvalues of its quadratic representation. This result is then exploited to derive similarity relations for vectors with respect to a general symmetric cone. For two positive deenite matrices X and Y , the square of the spectral geometric mean is similar to the matrix...

The covariance matrix estimation plays an important role in portfolio optimization and risk management. It is well-known that essentially a convex quadratic programming problem, which also special case of symmetric cone optimization. Accurate will lead to more reasonable asset weight allocation. However, some existing methods do not consider the influence time-varying factor on estimations. To ...

In this paper we present an improved neural network to solve strictly convex quadratic programming(QP) problem. The proposed model is derived based on a piecewise equation correspond to optimality condition of convex (QP) problem and has a lower structure complexity respect to the other existing neural network model for solving such problems. In theoretical aspect, stability and global converge...

We generalize primal-dual interior-point methods for linear programming problems to the convex optimization problems in conic form. Previously, the most comprehensive theory of symmetric primal-dual interior-point algorithms was given by Nesterov and Todd 8, 9] for the feasible regions expressed as the intersection of a symmetric cone with an aane subspace. In our setting, we allow an arbitrary...

A new class of preconditioners is proposed for the iterative solution of symmetric indefinite systems arising from interior-point methods. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail to provide sufficient accuracy unless appropriately preconditioned. Now we introduce two types of preconditione...

A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown—by several authors using different techniques—that the convex hull of the intersection of an ellipsoid, E , and a split disjunction, (l−xj)(xj−u) ≤ 0 with l < u, equals the intersection of E with an additional second-order-cone...

A common computational approach for polynomial optimization problems (POPs) is to use (hierarchies of) semidefinite programming (SDP) relaxations. When the variables in POP are required be nonnegative – as case combinatorial problems, example these SDP typically involve matrices, i.e. they conic over doubly cone. The Jordan reduction, a symmetry reduction method optimization, was recently intro...

It is known that the Karush-Kuhn-Tucker (KKT) conditions of semidefinite programming can be reformulated as a nonsmooth system via the metric projector over the cone of symmetric and positive semidefinite matrices. We show in this paper that the primal and dual constraint nondegeneracies, the strong regularity, the nonsingularity of the B-subdifferential of this nonsmooth system, and the nonsin...