The ε constrained method is an algorithm transformation method, which can convert algorithms for unconstrained problems to algorithms for constrained problems using the ε level comparison, which compares search points based on the pair of objective value and constraint violation of them. We have proposed the ε constrained differential evolution εDE, which is the combination of the ε constrained...

In this paper, we study scalable algorithms for influence maximization with general marketing strategies (IM-GMS), in which a marketing strategy mix is modeled as a vector x = (x1, . . . , xd) and could activate a node v in the social network with probability hv(x). The IM-GMS problem is to find the best strategy mix x∗ that maximize the influence spread due to influence propagation from the ac...

A unique game is a type of constraint satisfaction problem with two variables per constraint. The value of a unique game is the fraction of the constraints satisfied by an optimal solution. Khot (STOC’02) conjectured that for arbitrarily small γ,ε > 0 it is NPhard to distinguish games of value smaller than γ from games of value larger than 1− ε . Several recent inapproximability results rely on...

We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval [0, T/ε] for initial data of the form εU0, where T depends only on some Sobolev norm of U0. We show that for such data there exists a unique solution on a time interval [0, exp T/ε], provided that ε is sufficiently small. This is achieved by careful co...

In this paper, we study the theoretical properties of a class of iteratively re-weighted least squares (IRLS) algorithms for sparse signal recovery in the presence of noise. We demonstrate a one-to-one correspondence between this class of algorithms and a class of Expectation-Maximization (EM) algorithms for constrained maximum likelihood estimation under a Gaussian scale mixture (GSM) distribu...

We consider global convergence properties of the augmented Lagrangian methods on problems with degenerate constraints, with a special emphasis on mathematical programs with complementarity constraints (MPCC). In the general case, we show convergence to stationary points of the problem under an error bound condition for the feasible set (which is weaker than constraint qualifications), assuming ...

This work addresses the limits on the information that can be transmitted over the wireless channel under the conditions stated by the MAC layer: a selected scheduling discipline and an ensured level of QoS. Based on the effective bandwidth theory, the joint influence of the channel fading, the data outsourcing process, and the scheduling discipline in the QoS metrics are studied. We obtain a c...

Let Z(F ) be the number of solutions of a random k-satisfiability formula F with n variables and clause density α. Assume that the probability that F is unsatisfiable is O(1/ log(n)) for some δ > 0. We show that (possibly excluding a countable set of ‘exceptional’ α’s) the normalized logarithm of the number of solutions concentrates, i.e., there exists a non-random function α 7→ φs(α) such that...

We propose a first order interior point algorithm for a class of nonLipschitz and nonconvex minimization problems with box constraints, which arise from applications in variable selection and regularized optimization. The objective functions of these problems are continuously differentiable typically at interior points of the feasible set. Our first order algorithm is easy to implement and the ...