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In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
Incremental learning is a form of online learning. Incremental learning can modify the parameters and structure of the deep learning model so that the model does not forget the old knowledge while learning new knowledge. Preventing…
This paper investigates the control of nonlinear systems using a piecewise linear approximation framework. The proposed approach combines a PID controller with locally linearized models obtained by partitioning the nonlinear function into…
In this paper we propose a {\it discontinuous} plane wave neural network (DPWNN) method with $hp-$refinement for approximately solving Helmholtz equation and time-harmonic Maxwell equations. In this method, we define a quadratic functional…
The method presented extends a given regression neural network to make its performance improve. The modification affects the learning procedure only, hence the extension may be easily omitted during evaluation without any change in…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
The learning of predictive models for data-driven decision support has been a prevalent topic in many fields. However, construction of models that would capture interactions among input variables is a challenging task. In this paper, we…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
We propose a two-step estimating procedure for generalized additive partially linear models with clustered data using estimating equations. Our proposed method applies to the case that the number of observations per cluster is allowed to…
We propose two numerical algorithms in the fully nonconvex setting for the minimization of the sum of a smooth function and the composition of a nonsmooth function with a linear operator. The iterative schemes are formulated in the spirit…
The alternating minimization (AM) method is a fundamental method for minimizing convex functions whose variable consists of two blocks. How to efficiently solve each subproblems when applying the AM method is the most concerned task. In…
We propose an exact iterative algorithm for minimization of a class of continuous cell-wise linear convex functions on a hyperplane arrangement. Our particular setup is motivated by evaluation of so-called rank estimators used in robust…
The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their…
The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…