Successive element correction algorithms for sparse unconstrained optimization

Unconstrained Derivative-Free Optimization by Successive Approximation

We present an algorithmic framework for unconstrained derivative-free optimization based on dividing the search space in regions (partitions). Every partition is assigned a representative point. The representative points form a grid. A piece-wise constant approximation to the function subject to optimization is constructed using a partitioning and its corresponding grid. The convergence of the ...

Tensor Methods for Large, Sparse Unconstrained Optimization

Tensor methods for unconstrained optimization were rst introduced by Schn-abel and Chow SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate-size problems. The major contribution of this paper is the extension of these methods to large, sparse unconstrained optimization problems. This extension requires an entirely new way of solving the tensor model th...

Minimax Optimal Algorithms for Unconstrained Linear Optimization

We design and analyze minimax-optimal algorithms for online linear optimization games where the player’s choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark strategy. While the standard benchmark is the loss of the best strategy chosen from a bounded comparator set, we consider a very broad range of benchmark funct...

Successive column correction algorithms for solving sparse nonlinear systems of equations

Comparative Study of Bio-inspired algorithms for Unconstrained Optimization Problems

Nature inspired meta-heuristic algorithms are iterative search processes which find near optimal solutions by efficiently performing exploration and exploitation of the solution space. Considering the solution space in a specified region, this work compares performances of Bat, Cuckoo search and Firefly algorithms for unconstrained optimization problems. Global optima are found using various te...