This work is concerned with approximating constraint satisfaction problems (CSPs) with an additional global cardinality constraints. For example, Max Cut is a boolean CSP where the input is a graph G = (V, E) and the goal is to find a cut S ∪ S̄ = V that maximizes the number of crossing edges, |E(S , S̄ )|. The Max Bisection problem is a variant of Max Cut with an additional global constraint tha...

In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a (0.363− ε)-approximation algorithm, requiring only a single p...

For the spherical model with nearest-neighbour interactions, the microcanonical entropy s(ε,m) is computed analytically in the thermodynamic limit for all accessible values of the energy ε and the magnetization m per spin. The entropy is found to be a concave function, implying that the microcanonical and the canonical ensemble are equivalent, despite the long-range nature of the spherical cons...

This paper presents a filter-based artificial fish swarm algorithm for solving nonconvex constrained global optimization problems. Convergence to an ε-global minimizer is guaranteed. At each iteration k, the algorithm requires a (ρ(k),ε(k))-global minimizer of a bound constrained bi-objective subproblem, where as k→ ∞, ρ(k)→ 0 gives the constraint violation tolerance and ε(k)→ ε is the error bo...

We consider the rooted orienteering problem: Given a set P of n points in the plane, a starting point r ∈ P , and a length constraint B, one needs to find a path starting from r that visits as many points of P as possible and of length not exceeding B. We present a (1 − ε)-approximation algorithm for this problem that runs in nO(1/ε) time; the computed path visits at least (1 − ε)kopt points of...

Simulation-based design has become an inherent part of multidisciplinary design as simulation tools provide designers with a flexible and computationally efficient means to explore the interrelationships among various disciplines. Complications arise when the simulation programs may have deviations associated with input parameters (external uncertainties) as well as internal uncertainties due t...

We propose a novel idea of regression – balancing the distances from a regression function to all examples. We created a method, called balanced support vector regression (balanced SVR) in which we incorporated this idea to support vector regression (SVR) by adding an equality constraint to the SVR optimization problem. We implemented our method for two versions of SVR: ε-insensitive support ve...

We investigate the optimal portfolio deleveraging (OPD) problem with permanent and temporary price impacts, where objective is to maximize equity while meeting a prescribed debt/equity requirement. take real situation cross impact among different assets into consideration. The resulting is, however, nonconvex quadratic program constraint box constraint, which known be NP-hard. In this paper, we...

In this paper, we improve a result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a (1−ε)-satisfiable instance of Unique Games with the constraint graph G, our algorithm finds an assignment satisfying at least a 1 − Cε/hG fraction of all constraints if ε < cλG where hG is the edge expansion of G, λG is the second smallest eigenvalue...

The experimental value for the isospin amplitude ReA2 in K → ππ decays has been successfully explained within the standard model (SM), both within the large N approach to QCD and by QCD lattice calculations. On the other hand within the large N approach the value of ReA0 is by at least 30% below the data. While this deficit could be the result of theoretical uncertainties in this approach and c...