Infeasible Method Research Articles

Implementation of Music Genre Classifier Using KNN Algorithm

As music history grew, music began to diversify into different genres. Thisstudy aims to implement a music genre classifier using the KNN algorithm and a faster method. The KNN algorithm is accurate but with long execution time. This study implements a new method that can speed up the process of the KNN algorithm, and the K-means clustering algorithm inspires the idea. The dataset is preprocessed using the new idea. The program will select the song that is the centroid of the genre and use the method of the KNN to return the closest genre based on the distance from the test sample to the centroid. In conclusion, the new method did not perform well in accuracy but sped up the program. This study provides a great reference for the music genre classification problem in the machine learning domain. The study investigates an infeasible method in preprocessing data for the KNN algorithm optimization.

Penalty and Augmented Lagrangian Methods for Constrained DC Programming

In this paper, we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC programs in which the first convex component of the objective and constraints is the sum of a smooth and a nonsmooth function, and their second convex component is the supremum of finitely many convex smooth functions. The existing methods for this problem usually have a weak convergence guarantee or require a feasible initial point. Inspired by the recent work by Pang et al. [Pang J-S, Razaviyayn M, Alvarado A (2017) Computing B-stationary points of nonsmooth DC programs. Math. Oper. Res. 42(1):95–118.], in this paper, we propose two infeasible methods with a strong convergence guarantee for the considered problem. The first one is a penalty method that consists of finding an approximate D-stationary point of a sequence of penalty subproblems. We show that any feasible accumulation point of the solution sequence generated by such a penalty method is a B-stationary point of the problem under a weakest possible assumption that it satisfies a pointwise Slater constraint qualification (PSCQ). The second one is an augmented Lagrangian (AL) method that consists of finding an approximate D-stationary point of a sequence of AL subproblems. Under the same PSCQ condition as for the penalty method, we show that any feasible accumulation point of the solution sequence generated by such an AL method is a B-stationary point of the problem, and moreover, it satisfies a Karush–Kuhn–Tucker type of optimality condition for the problem, together with any accumulation point of the sequence of a set of auxiliary Lagrangian multipliers. We also propose an efficient successive convex approximation method for computing an approximate D-stationary point of the penalty and AL subproblems. Finally, some numerical experiments are conducted to demonstrate the efficiency of our proposed methods.

A trust‐region method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils

AbstractThe l parameterized generalized eigenvalue problems for the nonsquare matrix pencils, proposed by Chu and Golub [SIAM J. Matrix Anal. Appl., 28(2006), pp. 770‐787], can be formulated as an optimization problem on a corresponding complex product Stiefel manifold. Some early proposed algorithms are based on the first‐order information of the objective function, and fast convergence could not be expected. In this article, we turn the generic Riemannian trust‐region method of Absil et al. into a practical algorithm for solving the underlying problem, which enjoys the global convergence and local superlinear convergence rate. Numerical experiments are provided to illustrate the efficiency of the proposed method. Detailed comparisons with some existing results (l = 1 and l = n) are given first. For the case l = n, the algorithm can yield exactly the same optimal solution as Ito and Murota's algorithm, which is essentially a direct method to solve the problem. The algorithm runs faster than Boutry et al.'s algorithm for the case l = 1. Further comparisons with some early proposed gradient‐based algorithms, and some latest infeasible methods for solving manifold optimization problems are also provided to show the merits of the proposed approach.

The Data‐Driven Schrödinger Bridge

AbstractErwin Schrödinger posed—and to a large extent solved—in 1931/32 the problem of finding the most likely random evolution between two continuous probability distributions. This article considers this problem in the case when only samples of the two distributions are available. A novel iterative procedure is proposed, inspired by Fortet‐IPF‐Sinkhorn type algorithms. Since only samples of the marginals are available, the new approach features constrained maximum likelihood estimation in place of the nonlinear boundary couplings, and importance sampling to propagate the functions ϕ and solving the Schrödinger system. This method mitigates the curse of dimensionality, compared to the introduction of grids, which in high dimensions lead to numerically unfeasible methods. The methodology is illustrated in two applications: entropic interpolation of two‐dimensional Gaussian mixtures, and the estimation of integrals through a variation of importance sampling. © 2020 Wiley Periodicals LLC.

Clinical Concept Normalization on Medical Records Using Word Embeddings and Heuristics.

Electronic health records contain valuable information on patients' clinical history in the form of free text. Manually analyzing millions of these documents is unfeasible and automatic natural language processing methods are essential for efficiently exploiting these data. Within this, normalization of clinical entities, where the aim is to link entity mentions to reference vocabularies, is of utmost importance to successfully extract knowledge from clinical narratives. In this paper we present sieve-based models combined with heuristics and word embeddings and present results of our participation in the 2019 n2c2 (National NLP Clinical Challenges) shared-task on clinical concept normalization.

A new filter QP-free method for the nonlinear inequality constrained optimization problem

In this paper, a filter QP-free infeasible method with nonmonotone line search is proposed for minimizing a smooth optimization problem with smooth inequality constraints. This proposed method is based on the solution of nonsmooth equations, which are obtained by the Lagrangian multiplier method and the function of the nonlinear complementarity problem for the Karush–Kuhn–Tucker optimality conditions. Especially, each iteration of this method can be viewed as a perturbation of a Newton or quasi-Newton iteration on both the primal and dual variables for the solution of the Karush–Kuhn–Tucker optimality conditions. What is more, it is considered to use the function of the nonlinear complementarity problem in the filter, which makes the proposed algorithm avoid the incompatibility. Then the global convergence of the proposed method is given. And under some mild conditions, the superlinear convergence rate can be obtained. Finally, some preliminary numerical results are shown to illustrate that the proposed filter QP-free infeasible method is quite promising.

Considerations for waste gasification as an alternative to landfilling in Washington state using decision analysis and optimization

The United States is among the highest waste-producing nations in the world, but unlike many other developed nations, it processes only a fraction of its waste for recycling or energy production. The feasibility of alternatives to landfilling was explored using a multi-criteria decision-making model and a linear optimization model. Specifically, further development of waste gasification in Washington State was considered. In Washington, landfilling is still the primary form of waste management, resulting in significant environmental and social costs. The first stage of the analysis entailed the identification of the most effective gasification method for a plant located in Seattle with the objective of significant waste diversion from the largest waste processing site in Washington, the Roosevelt Regional Landfill. The Analytic Hierarchy Process (AHP) was employed to perform an objective comparison. This process ranked the gasification alternatives using various criteria and determined that steam gasification was superior to the other options, due to capacity and clean byproduct gases. Subsequently, a network optimization model was constructed to compare the cost of steam gasification and landfilling over a ten-year period, determining whether gasification plants would be viable in Seattle and Alaska. Results indicate that the Seattle gasification plant would be a superior option to current landfilling practices while an Alaska plant would be infeasible, in part due to the limited quantity of waste transported from Alaska to Roosevelt. Gasification methods will become more cost-effective as technology evolves, suggesting that currently infeasible methods have future potential.

3-1 Piecewise NCP Function for New Nonmonotone QP-Free Infeasible Method

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00260005/04.jpg"" width=""300"" />Algorithm flow chart</div> We propose a nonmonotone QP-free infeasible method for inequality-constrained nonlinear optimization problems based on a 3-1 piecewise linear NCP function. This nonmonotone QP-free infeasible method is iterative and is based on nonsmooth reformulation of KKT first-order optimality conditions. It does not use a penalty function or a filter in nonmonotone line searches. This algorithm solves only two systems of linear equations with the same nonsingular coefficient matrix, and is implementable and globally convergent without a linear independence constraint qualification or a strict complementarity condition. Preliminary numerical results are presented. </span>

An infeasible homotopy method for solving fixed point problems on a general unbounded set

In this paper, we consider an infeasible homotopy method to solve fixed point problems on a general unbounded set. The method enlarges the choice scope of initial points by a perturbation on equality constraint. Under a new and weaker condition for the defining mapping \(\Phi \), a constructive proof of the existence of fixed points and the global convergence are obtained. The computational result illustrates that our method improves greatly the computational efficiency than the existing interior point homotopy methods.

Interior hybrid proximal extragradient methods for the linear monotone complementarity problem

We present new infeasible path-following methods for linear monotone complementarity problems based on Auslender, Teboulle and Ben-Tiba’s log-quadratic barrier functions. The central paths associated with these barriers are always well defined and, for those problems which have a solution, convergent to a pair of complementary solutions. Starting points in these paths are easy to compute. The theoretical iteration-complexity of these new path-following methods is derived and improved by a strategy which uses relaxed hybrid proximal-extragradient steps to control the quadratic term. Encouraging preliminary numerical experiments are presented.

An infeasible QP-free method without a penalty function for nonlinear inequality constrained optimization

In this paper, we present a new QP-free method without using a penalty function for inequality constrained optimization. It is an infeasible method. At each iteration, three linear equations with the same coefficient matrix are solved. The nearly active set technique is used in the algorithm, which eliminates some inactive constraints and reduces the dimension of coefficient matrix, and thereby reduces the amount of computational work. Moreover, the algorithm reduces the value of objective function or the measure of constraints violation according to the relationship between optimality and feasibility. Under common conditions, we prove that the proposed method has global and superlinear local convergence. Lastly, preliminary numerical results are reported.

AN INFEASIBLE SSLE FILTER ALGORITHM FOR GENERAL CONSTRAINED OPTIMIZATION WITHOUT STRICT COMPLEMENTARITY

In this paper, we propose a new sequential systems of linear equations (SSLE) filter algorithm, which is an infeasible QP-free method. The new algorithm needs to solve a few reduced systems of linear equations with the same nonsingular coefficient matrix, and after finitely many iterations, only two linear systems need to be solved. Furthermore, the nearly active set technique is used to improve the computational effect. Under the linear independence condition, the global convergence is proved. In particular, the rate of convergence is proved to be one-step superlinear without assuming the strict complementarity condition. Numerical results and comparison with other algorithms indicate that the new algorithm is promising.

An infeasible nonmonotone SSLE algorithm for nonlinear programming

In this paper, we propose a new nonmonotone algorithm using the sequential systems of linear equations, which is an infeasible QP-free method. We use neither a penalty function nor a filter. Therefore, it is unnecessary to choose a problematic penalty parameter. The new algorithm only needs to solve three systems of linear equations with the same nonsingular coefficient matrix. Under some suitable conditions, the global convergence is established. Some numerical results are also presented.

Some non-interior path-following methods based on a scaled central path for linear complementarity problems

In this paper we present some non-interior path-following methods for linear complementarity problems. Instead of using the standard central path we use a scaled central path. Based on this new central path, we first give a feasible non-interior path-following method for linear complementarity problems. And then we extend it to an infeasible method. After proving the boundedness of the neighborhood, we prove the convergence of our method. Another point we should present is that we prove the local quadratic convergence of feasible method without the assumption of strict complementarity at the solution.

Is a Molecular Adiabatic Approximation Appropriate to Positronic Atoms and Molecules?

The adiabatic approximation to positronic atoms and molecules was considered as an option to the computationally unfeasible methods that treat all particles in a common footing, in two difierent approaches communicated in the 37th PSPA. Here we present further assessment and comparison of the two approaches as a way of evaluating the potential of adiabatic or, as we found preferable, molecular approaches.

A smoothing QP-free infeasible method for nonlinear inequality constrained optimization

In this paper, a smoothing QP-free infeasible method is proposed for nonlinear inequality constrained optimization problems. This iterative method is based on the solution of nonlinear equations which is obtained by the multipliers and the smoothing Fisher-Burmeister function for the KKT first-order optimality conditions. Comparing with other QP-free methods, this method does not request the strict feasibility of iteration. In particular, this method is implementable and globally convergent without assuming the strict complementarity condition and the isolatedness of accumulation points. Furthermore, the gradients of active constraints are not requested to be linearly independent. Preliminary numerical results indicate that this smoothing QP-free infeasible method is quite promising.

Sequential systems of linear equations method for general constrained optimization without strict complementarity

In this paper, based on an l 1 - l ∞ hybrid exact penalty function, we proposed an infeasible SSLE method for general constrained optimization. An automatic adjustment rule is incorporated in the algorithm for the choice of the penalty parameter, which ensures that the penalty parameter be updated only finitely many times. We also extend the Facchinei–Fischer–Kanzow active-set identification technique to general constrained optimization and a corresponding identification function is given. At each iteration, only two or three reduced linear equations with the same coefficients are solved to obtain the search direction. Under the linear independence condition, the sequence generated by the new algorithm globally converges to a KKT point. In particular, the convergence rate is proved to be one-step superlinear without assuming the strict complementarity and under a condition weaker than the strong second-order sufficiency condition. Some preliminary numerical results indicate that the new algorithm is quite promising.

A new optimization algotithm with application to nonlinear MPC

This paper investigates application of SQP optimization algorithms to nonlinear model predictive control. It considers feasible vs. infeasible path methods, sequential vs. simultaneous methods and reduced vs. full space methods. A new optimization algorithm coined rFOPT which remains feasibile with respect to inequality constraints is introduced. The suitable choices between these various strategies are assessed informally through a small CSTR case study. The case study also considers the effect various discretization methods have on the optimization problem.

Feasible Interior Methods Using Slacks for Nonlinear Optimization

A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the feasible method is effective for problems containing both equality and inequality constraints. The relationship between slack-based methods and traditional feasible methods is discussed. Numerical results using the KNITRO package show the relative performance of feasible versus infeasible interior point methods.

A feasible semismooth asymptotically Newton method for mixed complementarity problems

Semismooth Newton methods constitute a major research area for solving mixed complementarity problems (MCPs). Early research on semismooth Newton methods is mainly on infeasible methods. However, some MCPs are not well defined outside the feasible region or the equivalent unconstrained reformulations of other MCPs contain local minimizers outside the feasible region. As both these problems could make the corresponding infeasible methods fail, more recent attention is on feasible methods. In this paper we propose a new feasible semismooth method for MCPs, in which the search direction asymptotically converges to the Newton direction. The new method overcomes the possible non-convergence of the projected semismooth Newton method, which is widely used in various numerical implementations, by minimizing a one-dimensional quadratic convex problem prior to doing (curved) line searches. As with other semismooth Newton methods, the proposed method only solves one linear system of equations at each iteration. The sparsity of the Jacobian of the reformulated system can be exploited, often reducing the size of the system that must be solved. The reason for this is that the projection onto the feasible set increases the likelihood of components of iterates being active. The global and superlinear/quadratic convergence of the proposed method is proved under mild conditions. Numerical results are reported on all problems from the MCPLIB collection [8].