Quadratic Programming Approach Research Articles

Interval stochastic quadratic programming approach for municipal solid waste management

In this study, an interval stochastic quadratic programming method (ISQP) is developed through incorporating techniques of chance-constrained programming (CCP) and inexact quadratic programming (IQP) within a general framework. This method improves upon the conventional IQP approaches in uncertainty reflection and risk analysis. Interval stochastic quadratic programming can handle dual uncertainties expressed as interval values and probability distributions, and can deal with nonlinearities in objective function to reflect economies-of-scale effects on the system cost. It can also support the assessment of the risk of violating various constraints, for accomplishing a minimizing system cost. The developed ISQP is applied to a municipal solid waste (MSW) management system with multiple disposal facilities and multiple cities within multiple time periods. Results of the case study indicate that useful solutions for planning MSW management practices have been generated under different probability levels of violating constraints, which are informative and flexible for decision makers. A high system cost is associated with a low risk level of violating constraints, and a low system costs will run into a high probability of violating constraints. There is a tradeoff between the system cost and the constraint-violation risk.

An inexact Newton method for nonconvex equality constrained optimization

We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence of negative curvature without requiring information about the inertia of the primal–dual iteration matrix. Negative curvature may arise from second-order information of the problem functions, but in fact exact second derivatives are not required in the approach. The complete algorithm is characterized by its emphasis on sufficient reductions in a model of an exact penalty function. We analyze the global behavior of the algorithm and present numerical results on a collection of test problems.

Shape optimization of piezoelectric devices using an enriched meshfree method

AbstractWe present an enriched reproducing kernel particle method for shape sensitivity analysis and shape optimization of two‐dimensional electromechanical domains. This meshfree method incorporates enrichment functions for better representation of discontinuous electromechanical fields across internal boundaries. We use cubic splines for delineating the geometry of internal/external domain boundaries; and the nodal coordinates and slopes of these splines at their control points become the design parameters. This approach enables smooth manipulations of bi‐material interfaces and external boundaries during the optimization process. It also enables the calculation of displacement and electric‐potential field sensitivities with respect to the design parameters through direct differentiation, for which we adopt the classical material derivative approach. We verify this implementation of sensitivity calculations against an exact solution to a variant of Lamé's problem, and also, finite‐difference approximations. We follow a sequential quadratic programming approach to minimize the cost function; and demonstrate the utility of the overall technique through a model problem that involves the shape optimization of a piezoelectric fan. Copyright © 2008 John Wiley & Sons, Ltd.

Decision feedback data detection in frequency domain for single carrier cyclic prefix assisted CDMA systems: A sequential quadratic programming approach

This paper proposes a frequency domain decision feedback data receiver for the uplink transmission of broadband single carrier cyclic prefix-assisted CDMA systems. The optimum data detection problem based on the maximal-likelihood criteria for this system is addressed as a combinatorial optimization problem. A sequential quadratic programming approach is proposed to solve this problem. The parallel gradient projection method and projected successive over relaxation algorithm are proposed to solve the sequential quadratic programming problem, which corresponds to low-complexity nonlinear parallel and successive interference cancellation schemes in frequency domain. The convergence properties and the complexities of these methods are analyzed and compared with conventional methods. The simulation results show that, with a few iterations, the proposed scheme gives near single user performance even for fully loaded systems.

A NONINVASIVE DEMOGRAPHIC ASSESSMENT OF SEA LIONS BASED ON STAGE‐SPECIFIC ABUNDANCES

A pressing need exists to develop new approaches for obtaining information on demographic rates without causing further threats to imperiled animal populations. In this paper, we illustrate and apply a data-fitting technique based on quadratic programming that uses stage-specific abundance data to estimate demographic rates and asymptotic population growth rates (lambda). We used data from seven breeding colonies of California sea lions (Zalophus californianus) in the Gulf of California, Mexico. Estimates of lambda were similar to those from previous studies relying on a diffusion approximation using trends in total abundance. On average, predicted abundances were within 24% of the observed value for the inverse estimation method and within 29% of the observed value for the diffusion approximation. Our results suggest that three of the seven populations are declining (lambda < 1), but as many as six may be at risk. Elasticity and sensitivity analyses suggest that population management in most sites should focus on the protection of adults, whose survival generally contributes the most to lambda. The quadratic programming approach is a promising noninvasive technique for estimating demographic rates and assessing the viability of populations of imperiled species.

An inexact stochastic quadratic programming method for municipal solid waste management

The existences of nonlinearities and uncertainties are the main complexities that cause difficulties in planning municipal solid waste-management systems. In this study, an inexact stochastic quadratic programming method is developed for handling nonlinearities in the cost objective to reflect the economies of scale and uncertainties expressed as probability distributions and discrete intervals. This model improves upon the conventional inexact quadratic programming and two-stage stochastic programming approaches. It can better reflect system cost variations and generate more reasonable and applicable solutions. It can also be used for analysing various policy scenarios that are associated with different levels of penalties when the promised policy targets are violated. The developed method is applied to a case of long-term waste-management planning. The interactive and derivative algorithms are employed for solving the developed model. The solutions are presented as combinations of deterministic, interval and distributional information. They can be used for generating decision alternatives and thus help waste managers to identify desired policies under various environmental, economic and system-reliability constraints.

Evaluating Directionally-Sensitive Multivariate Control Charts with an Application to Biosurveillance

The main goal of biosurveillance is the early detection of disease outbreaks. Advances in technology have allowed the collection, transfer, and storage of pre-diagnostic information in addition to traditional diagnostic data. Such data carry the potential of an earlier outbreak signature. In this work we deal with monitoring multivariate time series of daily counts. Current temporal monitoring in biosurveillance is done univariately by applying control charts to each time series separately. However, monitoring via multivariate control charts has the potential of greatly reducing false alert rates and increasing true alert rates. Classical multivariate control charts are aimed at detecting shifts in the vector of means in any direction. Whereas one-side univariate control charts are easy to obtain from their two-sided counterpart, directional sensitivity in the multivariate case is non trivial. Several approaches were suggested for obtaining directionally-sensitive multivariate Shewhart chart (commonly referred to as Hotelling T2 charts). However, there has not been an extensive comparison of these methods and it is not clear which approach performs better. In this work we compare two computational-feasible approaches suggested in the literature, namely Follmann's simple correction and Testik and Runger's (TR) quadratic programming approach. In addition to their proposed directionally sensitive Hotelling charts we derive directionally sensitive Multivariate EWMA (MEWMA) charts. We then perform an extensive analysis of the performance the four methods, where we examine model performance in terms of true and false detection, robustness to assumptions, training data length and sensitivity to data characteristics. Our results show that TR's approach performs slightly better for normally distributed data, yet Follmann's approach is more robust to normality and independence assumptions.

A One-Layer Recurrent Neural Network With a Discontinuous Hard-Limiting Activation Function for Quadratic Programming

In this paper, a one-layer recurrent neural network with a discontinuous hard-limiting activation function is proposed for quadratic programming. This neural network is capable of solving a large class of quadratic programming problems. The state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints. In addition, a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming. Simulation results on numerical examples and support vector machine (SVM) learning show the effectiveness and performance of the neural network.

ROBUST POLE PLACEMENT VIA REFLECTION AXES POLYTOPES

A robust version of the output controller design for discrete-time systems is introduced. Instead of a single stable point a stable polytope is preselected in the closed loop characteristic polynomial coefficient space. A constructive procedure for generating stable polytopes is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure is quite straightforward because for a special family of polynomials the linear cover of so-called reflection vectors is stable. The roots placement of reflection vectors is studied. A stability measure in a polytope is introduced in order to solve the problem by quadratic programming approach.

Low-Sidelobe Multimode Horn Design for Circular Coverage Based on Quadratic Programming Approach

To obtain a broad circular-coverage beam with low sidelobe, this paper proposes optimization design based on the quadratic programming approach for circular horns. The desired excitation coefficients of higher-order modes are pre-determined and also evaluated by calculating universal radiation patterns. We show a design example of a multimode horn which has circular-coverage beam with low sidelobe level of about-30dB. The effectiveness of the designed horn is discussed by evaluating VSWR and radiation characteristics in X-band numerically and experimentally.

Kinematic Analysis of a Macro–Micro Redundantly Actuated Parallel Manipulator

In this paper the kinematic and Jacobian analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of the next generation of giant radio telescopes. This structure is composed of two parallel and redundantly actuated manipulators at the macro and micro level, which both are cable-driven. Inverse and forward kinematic analysis of this structure is presented in this paper. Furthermore, the Jacobian matrices of the manipulator at the macro and micro level are derived, and a thorough singularity and sensitivity analysis of the system is presented. The kinematic and Jacobian analysis of the macro–micro structure is extremely important to optimally design the geometry and characteristics of the LAR structure. The optimal location of the base and moving platform attachment points in both macro and micro manipulators, singularity avoidance of the system in nominal and extreme maneuvers, and geometries that result in high dexterity measures in the design are among the few characteristics that can be further investigated from the results reported in this paper. Furthermore, the availability of the extra degrees of freedom in a macro–micro structure can result in higher dexterity provided that this redundancy is properly utilized. In this paper, this redundancy is used to generate an optimal trajectory for the macro–micro manipulator, in which the Jacobian matrices derived in this analysis are used in a quadratic programming approach to minimize performance indices like minimal micro manipulator motion or singularity avoidance criterion.

Inexact Multistage Stochastic Quadratic Programming Method for Planning Water Resources Systems under Uncertainty

An inexact multistage stochastic quadratic programming (IMQP) method was developed for supporting water resources management under uncertainty. The IMQP method improves upon the existing multistage programming and inexact quadratic programming approaches, and can directly tackle uncertainties presented as interval numbers and probability distributions within a multistage context. Moreover, it can accommodate real-time dynamics of system uncertainties based on a complete set of scenarios; it can also deal with non-linearities in the objective function to reflect the effects of marginal utility on system benefits and costs. Because penalties are exercised with recourse against any infeasibility, the IMQP can support the analysis of various policy scenarios that are associated with different levels of economic consequences when the promised water-allocation targets are violated. The developed method was applied to the planning of water resources management in the Heshui River Basin, China. The results are us...

Novel quadratic programming approach for time series clustering with biomedical application

Fundamental problems in data mining mainly involve discrete decisions based on numerical analyses of data (e.g., class assignment, feature selection, data categorization, identifying outlier samples). These decision-making problems in data mining are combinatorial in nature and can naturally be formulated as discrete optimization problems. One of the most widely studied problems in data mining is clustering. In this paper, we propose a new optimization model for hierarchical clustering based on quadratic programming and later show that this model is compact and scalable. Application of this clustering technique in epilepsy, the second most common brain disorder, is a case point in this study. In our empirical study, we will apply the proposed clustering technique to treatment problems in epilepsy through the brain dynamics analysis of electroencephalogram (EEG) recordings. This study is a proof of concept of our hypothesis that epileptic brains tend to be more synchronized (clustered) during the period before a seizure than a normal period. The results of this study suggest that data mining research might be able to revolutionize current diagnosis and treatment of epilepsy as well as give a greater understanding of brain functions (and other complex systems) from a system perspective.

Fast quadratic programming approach for large scale reactive power optimization

A fast quadratic programming approach has been developed to control the reactive power (VAR) generation in dispatching centers. The main objective of VAR control is to minimize the transmission losses taking into consideration the voltage constraints at each node of the network. The developed approach utilizes the decomposition of whole system into smaller subsystems and coordination of different subsystem solutions to obtain the optimal VAR control in the large scale systems. The smallest practical size of the decomposed subsystems is the one-generator-bus subsystem. The fast and non-iterative VAR optimization of the decomposed subsystems is obtained based on considering only one active constraint at a time by solving the quadratic programming sub-problems. The numerical test results of IEEE-118 and 200 buses power system have indicated that the speed and accuracy of the proposed approach are adequate for real-time applications on large-scale systems. This approach is also applicable for large system deviations from its normal conditions and needs small memory size.

Generator estimation of Markov jump processes

Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. [D.T. Crommelin, E. Vanden-Eijnden, Fitting timeseries by continuous-time Markov chains: a quadratic programming approach, J. Comp. Phys. 217 (2006) 782–805]), a resolvent method (cf. [T. Müller, Modellierung von Proteinevolution, PhD thesis, Heidelberg, 2001]), and various implementations of an expectation-maximization algorithm ([S. Asmussen, O. Nerman, M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Stat. 23 (1996) 419–441; I. Holmes, G.M. Rubin, An expectation maximization algorithm for training hidden substitution models, J. Mol. Biol. 317 (2002) 753–764; U. Nodelman, C.R. Shelton, D. Koller, Expectation maximization and complex duration distributions for continuous time Bayesian networks, in: Proceedings of the twenty-first conference on uncertainty in AI (UAI), 2005, pp. 421–430; M. Bladt, M. Sørensen, Statistical inference for discretely observed Markov jump processes, J.R. Statist. Soc. B 67 (2005) 395–410]). Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.

On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem

In this paper, a multiobjective quadratic programming problem fuzzy random coefficients matrix in the objectives and constraints and the decision vector are fuzzy variables is considered. First, we show that the efficient solutions fuzzy quadratic multiobjective programming problems series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. An application fuzzy portfolio optimization problem as a convex quadratic programming approach is discussed and an acceptable solution to such problem is given. At the end, numerical examples are illustrated in the support of the obtained results.

A quadratic programming approach to the multi-product newsvendor problem with side constraints

A quadratic programming approach is proposed for solving the newsvendor problem with side constraints. Among its salient features are the facts that it: utilizes familiar packages to solve the problem such as Excel Solver and Lingo, can accommodate lower bounds of product’s demands that are larger than zero, and facilitates the performance of sensitivity analysis tasks.

Duality and the Computation of Approximate Invariant Densities for Nonsingular Transformations

We investigate a class of optimization problems which arise in the approximation of invariant densities for a nonsingular, measurable transformation T acting on a finite measure space. The problems under consideration have convex integral-type objectives and finite moment constraints and include, for example, the maximum entropy and quadratic programming approaches previously studied in the literature. This article is a natural sequel to those investigations and to the paper [C. Bose and R. Murray, Discrete Contin. Dyn. Syst., 14 (2006), pp. 597–615], where a general class of convergent moment approximations were defined such that the limiting optimal solution is an invariant density for T. This article mainly concerns the solution of a single finite moment problem arising from this general approximation scheme. Both theoretical aspects and computational issues are treated. Although the problem fits easily into the standard theory of duality in convex optimization, its dynamical origins lead to technical obstructions in the derivation of optimality conditions. In particular, the dual functional for our problem is neither strictly convex nor coercive, relating in part to the fact that the moment generating functions for the approximation scheme need not be pseudo-Haar. The method of the paper circumvents these obstructions and yields an unexpected benefit: each finite moment approximation leads to rigorous bounds on the support of all invariant densities for T.

A quadratic programming approach to the Randić index

Let G( k, n) be the set of connected graphs without multiple edges or loops which have n vertices and the minimum degree of vertices is k. The Randić index χ = χ( G) of a graph G is defined by χ ( G ) = ∑ ( uv ) ( δ u δ v ) - 1 / 2 , where δ u is the degree of vertex u and the summation extends over all edges ( uv) of G. Caporossi et al. [G. Caporossi, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs IV: Chemical trees with extremal connectivity index, Computers and Chemistry 23 (1999) 469–477] proposed the use of linear programming as one of the tools for finding the extremal graphs. In this paper we introduce a new approach based on quadratic programming for finding the extremal graphs in G( k, n) for this index. We found the extremal graphs or gave good bounds for this index when the number n k of vertices of degree k is between n − k and n. We also tried to find the graphs for which the Randić index attained its minimum value with given k ( k ⩽ n/2) and n. We have solved this problem partially, that is, we have showed that the extremal graphs must have the number n k of vertices of degree k less or equal n − k and the number of vertices of degree n − 1 less or equal k.

Solution of the input-constrained LQR problem using dynamic programming

The input-constrained LQR problem is addressed in this paper; i.e., the problem of finding the optimal control law for a linear system such that a quadratic cost functional is minimised over a horizon of length N subject to the satisfaction of input constraints. A global solution (i.e., valid in the entire state space) for this problem, and for arbitrary horizon N, is derived analytically by using dynamic programming. The scalar input case is considered in this paper. Solutions to this problem (and to more general problems: state constraints, multiple inputs) have been reported recently in the literature, for example, approaches that use the geometric structure of the underlying quadratic programming problem and approaches that use multi-parametric quadratic programming techniques. The solution by dynamic programming proposed in the present paper coincides with the ones obtained by the aforementioned approaches. However, being derived using a different approach that exploits the dynamic nature of the constrained optimisation problem to obtain an analytical solution, the present result complements the previous methods and reveals additional insights into the intrinsic structure of the optimal solution.