Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection. Secondly, to obtain centered solutions for systems of … Read more
For reducing costs of market frictions, investors need to build a small-scale portfolio by solving a cardinality constrained portfolio selection problem which is NP-hard in general and not easy to be solved eciently for a large-scale problem. In this paper, we propose a penalty proximal alternat- ing linearized minimization method for the large-scale problems in … Read more
This paper studies $K$-sublinear inequalities, a class of inequalities with strong relations to K-minimal inequalities for disjunctive conic sets. We establish a stronger result on the sufficiency of $K$-sublinear inequalities. That is, we show that when $K$ is the nonnegative orthant or the second-order cone, $K$-sublinear inequalities together with the original conic constraint are always … Read more
In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any member of the Broyden convex class of updates. Our proposed method makes use of efficient updates to the QR factorization that … Read more
In this note, we prove that the KKT mapping for nonlinear semidefinite optimization problem is upper Lipschitz continuous at the KKT point, under the second-order sufficient optimality conditions and the strict Robinson constraint qualification. ArticleDownload View PDF
What happens to the conclusion of the Ekeland variational principle (briefly, EVP) if a considered function $f:X\to \R\cup\{+\infty\}$ is lower semicontinuous not on a whole metric space $X$ but only on its domain? We provide a straightforward proof showing that it still holds but only for $\epsilon $ varying in some interval $]0,\beta-\inf_Xf[$, where $\beta$ … Read more
An unconditionally energy stable time stepping scheme is introduced to solve Cahn-Morral-like equations in the present study. It is constructed based on the combination of David Eyre’s time stepping scheme and Schur complement approach. Although the presented method is general and independent to the choice of homogeneous free energy density function term, logarithmic and polynomial … Read more
We deal with chance constrained problems (CCP) with differentiable nonlinear random functions and discrete distribution. We allow nonconvex functions both in the constraints and in the objective. We reformulate the problem as a mixed-integer nonlinear program, and relax the integer variables into continuous ones. We approach the relaxed problem as a mathematical problem with complementarity … Read more
We develop fully polynomial time $(\Sigma,\Pi)$-approximation schemes for stochastic dynamic programs with continuous state and action spaces, when the single-period cost functions are convex Lipschitz-continuous functions that are accessed via value oracle calls. That is, for every given additive error parameter $\Sigma>0$ and multiplicative error factor $\Pi=1+\epsilon>1$, the scheme returns a feasible solution whose value … Read more
In this paper, we consider a class of finite-sum convex optimization problems whose objective function is given by the summation of $m$ ($\ge 1$) smooth components together with some other relatively simple terms. We first introduce a deterministic primal-dual gradient (PDG) method that can achieve the optimal black-box iteration complexity for solving these composite optimization … Read more