In this paper, an efficient modification of homotopy perturbation method, namely optimal homotopy perturbation method, is introduced for solving linear and nonlinear partial differential equations with large solution domain based on a new homotopy perturbation method and Padé approximation method. We compare the performance of the method with those of new homotopy perturbation and optimal varia...

The exploration-exploitation tradeoff is among the central challenges of reinforcement learning. A hypothetical exact Bayesian learner would provide the optimal solution, but is intractable in general. I show that, however, in the specific case of Gaussian process inference, it is possible to make analytic statements about optimal learning of both rewards and transition dynamics, for nonlinear,...

In this paper we propose a novel text summarization model, the redundancy-constrained knapsack model. We add to the Knapsack problem a constraint to curb redundancy in the summary. We also propose a fast decoding method based on the Lagrange heuristic. Experiments based on ROUGE evaluations show that our proposals outperform a state-of-the-art text summarization model, the maximum coverage mode...

This paper develops a solution strategy for two-stage stochastic programs with integer recourse. The proposed methodology relies on approximating the underlying stochastic program via sampling, and solving the approximate problem via a specialized optimization algorithm. We show that the proposed scheme will produce an optimal solution to the true problem with probability approaching one expone...

In this paper an approximation scheme is developed for the solution of the linear quadratic Gaussian (LQG) control on a finite time interval for hereditary systems with multiple noncommensurate delays and distributed delay. The solution here proposed is achieved by means of two approximating subspaces: the first one to approximate the Riccati equation for control and the second one to approxima...

In this paper, a new approach based on embedding method for finding an approximate solution for a wide range of nonlinear optimal control problems with delays in state and control variables subject to mixed-control state constraints is introduced. First, the problem is transformed to a new optimal measure problem which is an infinite dimensional linear programming problem and then this new prob...

Assume that A and B are non-void subsets of a metric space, and that S : A −→ B and T : A −→ B are given non-self mappings. In light of the fact that S and T are non-self mappings, it may happen that the equations Sx = x and Tx = x have no common solution, named a common fixed point of the mappings S and T . Subsequently, in the event that there is no common solution of the preceding equations,...

In this paper, a regulation control problem for constrained nonlinear systems with quantized inputs is formulated as a Model Predictive Control (MPC) problem. The MPC problem is represented as a multi-parametric Nonlinear Integer Programming (mp-NIP) problem and a computational method to find an explicit approximate solution of this problem is considered. It consists in constructing a feasible ...

The single-stage scheduling problem to minimize the makespan of identical jobs on uniform parallel machines is known to be solvable in polynomial-time. We extend this work to consider multi-stage systems with flowshop configuration. We show that the 2-stage problem may also be solved in polynomial-time and for the number of stages greater than two, the problem is shown to be NP-hard. We present...

In the paper, the question is investigated if a bundle algorithm can be used to compute approximate solutions for bilevel programming problems where the lower level optimal solution is in general not uniquely determined. To give a positive answer to this question, an appropriate regularization approach is used in the lower level. In the general case, the resulting algorithm computes an approxim...