An alternative approach to understanding second-order conditions for constrained optimization - lagrange multipliers

This paper presents an alternative approach to solving a standard problem, frequently encountered in advanced microeconomics, using the technique of Lagrange multipliers. The objective is to enhance the understanding of students as to the derivation of the second-order conditions.

Bearing-only localization using geometrically constrained optimization

We examine the problem of optimal bearing-only localization of a single target using synchronous measurements from multiple sensors. We approach the problem by forming geometric relationships between the measured parameters and their corresponding errors in the relevant emitter localization scenarios. Specifically, we derive a geometric constraint equation on the measurement errors in such a scenario. Using this constraint, we formulate the localization task as a constrained optimization problem that can be performed on the measurements in order to provide the optimal values such that the solution is consistent with the underlying geometry. We illustrate and confirm the advantages of our approach through simulation, offering detailed comparison with traditional maximum likelihood (TML) estimation.

Optimization of gaussian fuzzy membership functions and evaluation of the monotonicity property of fuzzy inference systems

In this paper, two issues relating to modeling of a monotonicity-preserving Fuzzy Inference System (FIS) are examined. The first is on designing or tuning of Gaussian Membership Functions (MFs) for a monotonic FIS. Designing Gaussian MFs for an FIS is difficult because of its spreading and curvature characteristics. In this study, the sufficient conditions are exploited, and the procedure of designing Gaussian MFs is formulated as a constrained optimization problem. The second issue is on the testing procedure for a monotonic FIS. As such, a testing procedure for a monotonic FIS model is proposed. Applicability of the proposed approach is demonstrated with a real world industrial application, i.e., Failure Mode and Effect Analysis. The results obtained are analysis and discussed. The outcomes show that the proposed approach is useful in designing a monotonicity-preserving FIS model.

Passive angle measurement based localization consistency via geometric constraints

In this paper, we examine the geometric relations between various measured parameters and their corresponding errors in angle-measurement based emitter localization scenarios. We derive a geometric constraint formulating the relationship among the measurement errors in such a scenario. Using this constraint, we formulate the localization task as a constrained optimization problem that can be performed on the measurements in order to provide the optimal values such that the solution is consistent with the underlying geometry.

Nonlinear discrimination using support vector machine

Appropriate training data always play an important role in constructing an efficient classifier to solve the data mining classification problem. Support Vector Machine (SVM) is a comparatively new approach in constructing a model/classifier for data analysis, based on Statistical Learning Theory (SLT). SVM utilizes a transformation of the basic constrained optimization problem compared to that of a quadratic programming method, which can be solved parsimoniously through standard methods. Our research focuses on SVM to classify a number of different sizes of data sets. We found SVM to perform well in the case of discrimination compared to some other existing popular classifiers.

Exploiting geometry for improved hybrid AOA/TDOA-based localization

In this paper we examine the geometrically constrained optimization approach to localization with hybrid bearing (angle of arrival, AOA) and time difference of  arrival (TDOA) sensors. In particular, we formulate a constraint on the measurement errors which is then used along with constraint-based optimization tools in order to estimate the maximum likelihood values of the errors given an appropriate cost function. In particular we focus on deriving a localization algorithm for stationary target localization in the so-called adverse localization geometries where the relative positioning of the sensors and the target do not readily permit accurate or convergent localization using traditional approaches. We illustrate this point via simulation and we compare our approach to a number of different techniques that are discussed in the literature.

Text document clustering with metric learning

One reason for semi-supervised clustering fail to deliver satisfactory performance in document clustering is that the transformed optimization problem could have many candidate solutions, but existing methods provide no mechanism to select a suitable one from all those candidates. This paper alleviates this problem by posing the same task as a soft-constrained optimization problem, and introduces the salient degree measure as an information guide to control the searching of an optimal solution. Experimental results show the effectiveness of the proposed method in the improvement of the performance, especially when the amount of priori domain knowledge is limited.

Multiple emitter localization using range only measurements considering geometrical constraints

This paper proposes a constrained optimization approach to improve the accuracy of a Time-of-Arrival (ToA) based multiple target localization system. Instead of using an overdetermined measurement system, this paper uses local distance measurements between the targets/emitters as the geometric constraint.Computer simulations are used to evaluate the performance of the geometrically constrained optimization method.

Stabilizing l1-norm prediction models by supervised feature grouping

Emerging Electronic Medical Records (EMRs) have reformed the modern healthcare. These records have great potential to be used for building clinical prediction models. However, a problem in using them is their high dimensionality. Since a lot of information may not be relevant for prediction, the underlying complexity of the prediction models may not be high. A popular way to deal with this problem is to employ feature selection. Lasso and l1-norm based feature selection methods have shown promising results. But, in presence of correlated features, these methods select features that change considerably with small changes in data. This prevents clinicians to obtain a stable feature set, which is crucial for clinical decision making. Grouping correlated variables together can improve the stability of feature selection, however, such grouping is usually not known and needs to be estimated for optimal performance. Addressing this problem, we propose a new model that can simultaneously learn the grouping of correlated features and perform stable feature selection. We formulate the model as a constrained optimization problem and provide an efficient solution with guaranteed convergence. Our experiments with both synthetic and real-world datasets show that the proposed model is significantly more stable than Lasso and many existing state-of-the-art shrinkage and classification methods. We further show that in terms of prediction performance, the proposed method consistently outperforms Lasso and other baselines. Our model can be used for selecting stable risk factors for a variety of healthcare problems, so it can assist clinicians toward accurate decision making.

A QoE centric distributed caching approach for vehicular video streaming in cellular networks

Distributed caching-empowered wireless networks can greatly improve the efficiency of data storage and transmission and thereby the users' quality of experience (QoE). However, how this technology can alleviate the network access pressure while ensuring the consistency of content delivery is still an open question, especially in the case where the users are in fast motion. Therefore, in this paper, we investigate the caching issue emerging from a forthcoming scenario where vehicular video streaming is performed under cellular networks. Specifically, a QoE centric distributed caching approach is proposed to fulfill as many users' requests as possible, considering the limited caching space of base stations and basic user experience guarantee. Firstly, a QoE evaluation model is established using verified empirical data. Also, the mathematic relationship between the streaming bit rate and actual storage space is developed. Then, the distributed caching management for vehicular video streaming is formulated as a constrained optimization problem and solved with the generalized-reduced gradient method. Simulation results indicate that our approach can improve the users' satisfaction ratio by up to 40%.

Cutting angle method - a tool for constrained global optimization

Cutting angle method (CAM) is a deterministic global optimization technique applicable to Lipschitz functions f: Rn → R. The method builds a sequence of piecewise linear lower approximations to the objective function f. The sequence of solutions to these relaxed problems converges to the global minimum of f. This article adapts CAM to the case of linear constraints on the feasible domain. We show how the relaxed problems are modified, and how the numerical efficiency of solving these problems can be preserved. A number of numerical experiments confirms the improved numerical efficiency.

New cutting-planes for the time-and/or precedence-constrained ATSP and directed VRP

In this paper, we introduce five classes of new valid cutting planes for the precedence-constrained (PC) and/or time-window-constrained (TW) Asymmetric Travelling Salesman Problems (ATSPs) and directed Vehicle Routing Problems (VRPs). We show that all five classes of new inequalities are facet-defining for the directed VRP-TW, under reasonable conditions and the assumption that vehicles are identical. Similar proofs can be developed for the VRP-PC. As ATSP-TW and PC-ATSP can be formulated as directed identical-vehicle VRP-TW and PC-VRP, respectively, this provides a link to study the polyhedral combinatorics for the ATSP-TW and PC-ATSP. The first four classes of these new cutting planes are cycle-breaking inequalities that are lifted from the well-known D^-_k and D⁺_k inequalities (see Grötschel and Padberg in Polyhedral theory. The traveling salesman problem: a guided tour of combinatorial optimization, Wiley, New York, 1985). The last class of new cutting planes, the TW ₂ inequalities, are infeasible-path elimination inequalities. Separation of these constraints will also be discussed. We also present prelimanry numerical results to demonstrate the strengh of these new cutting planes.

Constrained coordinated distributed control of smart grid with asynchronous information exchange

Smart grid constrained optimal control is a complex issue due to the constant growth of grid complexity and the large volume of data available as input to smart device control. In this context, traditional centralized control paradigms may suffer in terms of the timeliness of optimization results due to the volume of data to be processed and the delayed asynchronous nature of the data transmission. To address these limits of centralized control, this paper presents a coordinated, distributed algorithm based on distributed, local controllers and a central coordinator for exchanging summarized global state information. The proposed model for exchanging global state information is resistant to fluctuations caused by the inherent interdependence between local controllers, and is robust to delays in information exchange. In addition, the algorithm features iterative refinement of local state estimations that is able to improve local controller ability to operate within network constraints. Application of the proposed coordinated, distributed algorithm through simulation shows its effectiveness in optimizing a global goal within a complex distribution system operating under constraints, while ensuring network operation stability under varying levels of information exchange delay, and with a range of network sizes.

Dynamic prediction models and optimization of polyacrylonitrile (PAN) stabilization processes for production of carbon fiber

Thermal stabilization process of polyacrylonitrile (PAN) is the slowest and the most energy-consuming step in carbon fiber production. As such, in industrial production of carbonfiber, this step is considered as amajor bottleneck in the whole process. Stabilization process parameters are usually many in number and highly constrained, leading to high uncertainty. The goal of this paper is to study and analyze the carbon fiber thermal stabilization process through presenting several effective dynamic models for the prediction of the process. The key point with using dynamic models is that using an evolutionary search technique, the heat of reaction can be optimized. The employed components of the study are Levenberg–Marquardt algorithm (LMA)-neural network (LMA-NN), Gauss–Newton (GN)-curve fitting, Taylor polynomial method, and a genetic algorithm. The results show that the procedure can effectively optimize a given PAN fiber heat of reaction based on determining the proper values of heating rampand temperature