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...

We describe three algorithms for solving differentiable convex optimization problems constrained to simple sets in Rn, i.e., sets on which it is easy to project an arbitrary point. The first two algorithms are optimal in the sense that they achieve an absolute precision of ε in relation to the optimal value in O(1/ √ ε) iterations using only first order information. This complexity depends on a...

the thermo-hydraulic behavior of the air flow over a two dimensional ribbed channel wasnumerically investigated in various rib-width ratio configurations (b/h=0.5-1.75) atdifferent reynolds numbers, ranging from 6000 to 18000. the capability of differentturbulence models, including standard k-ε, rng k-ε, standard k-ω, and sst k-ω, inpredicting the heat transfer rate was compared with the experi...

In general, microgrids have a high renewable energy abandonment rate and grid construction operation costs. To improve the microgrid utilization rate, economic advantages, environmental safety of power operation, we propose hybrid storage capacity optimization method for wind–solar–diesel grid-connected system, based on an augmented ε- constraint method. First, battery is coupled with seasonal ...

In this paper, we propose a smoothing augmented Lagrangian method for finding a stationary point of a nonsmooth and nonconvex optimization problem. We show that any accumulation point of the iteration sequence generated by the algorithm is a stationary point provided that the penalty parameters are bounded. Furthermore, we show that a weak version of the generalized Mangasarian Fromovitz constr...

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual converg...

We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier—augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modifi...

The Mesh Adaptive Direct Search algorithm (MADS) is an iterative method for constrained blackbox optimization problems. One of the optional MADS features is a versatile search step in which quadratic models are built leading to a series of quadratically constrained quadratic subproblems. This work explores different algorithms that exploit the structure of the quadratic models: the first one ap...