We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a submodular function break submodularity. Say that F is ε-approximately submodular if there exists a submodular function f such that (1−ε)f(S) ≤ F (S) ≤ (1+ε)f(S) for ...

where w = ((ei)i≥0, (fi)i≥0 ) are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function y i = Cx w i , i ≥ 0. Let ε be a tolerance index on the output. The disturbance w is said to be ε-admissible if ‖y i −yi‖ ≤ ε, ∀ i ≥ 0, where (yi)i≥0 is the output signal associated with the case of an uninfected system. The set ...

We present a Lagrangian decomposition algorithmwhich uses logarithmic potential reduction to compute an ε-approximate solution of the general max-min resource sharing problem with M nonnegative concave constraints on a convex set B. We show that this algorithm runs in O(M(ε+lnM)) iterations, a data independent bound which is optimal up to polylogarithmic factors for any fixed relative accuracy ...

1. Abstract A novel strategy for handling the molding constraint for cast parts is presented. In a first step, a simple projection method for the velocity field is applied. If the optimized shape violates thickness constraints, this projection method is no longer sufficient and a general molding constraint is applied at the same time with thickness control. We apply an augmented Lagrangian meth...

We consider probabilistically constrained problems, in which the multivariate random variables are located in the right-hand sides. The objective function is linear, and its optimization is subject to a set of linear constraints as well as a joint probabilistic constraint enforcing that the joint fulfillment of a system of linear inequalities with random right-hand side variables be above a pre...

As there are many methods designed for augmented reality, it is still hard to really bring augmented reality application to the real life due to the performance constraint of mobile devices. In this project, I tried to implement certain promising algorithms and explore the possibilities of rich augmented reality application. ESM algorithm is chosen for tracking the clue of the scene together wi...

Dynamic detection and elimination of symmetry in constraints, is in general a hard task, but in Not-Equals binary constraint networks, the symmetry conditions can be simplified. In this paper, we extend the principle of symmetry to dominance in Not-Equals Constraint Networks and show how dominated values are detected and eliminated at each node of the search tree. A Linear time complexity algor...

Regularized and stabilized sequential quadratic programming methods are two classes of sequential quadratic programming (SQP) methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that provides a strong connection between augmented Lagrangian methods and...

We consider maximizing a monotone submodular function under a cardinality constraint or a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access to only a small fraction of the data stored in primary memory. We propose the following streaming algorithms taking O(ε) passes: 1. a (1 − e − ε)-approximation al...