Quadratic Programming Approach Research Articles

An Optimization Model for the Increment in the Yield of Distillation Columns Based on Reverse Engineering in the Petroleum Industry

Optimization in the chemical and petroleum industry is gaining increased interest because of its importance in maintaining product quality and enhancing production levels while improving profit margins. In this article, simulation of the atmospheric distillation unit of an existing petroleum refinery is carried out. Optimization was performed on the prepared simulation through the use of a sequential quadratic programming approach (SQP). The objective function consisted of energy minimization and production level maximization. The results obtained from optimization were implemented on the real process and it was demonstrated that the suggested changes increased overhead production levels and maintained product quality. Furthermore, a net economical balance between the increment of overhead products and the energy consumption showed an energy savings in the refinery.

Linear and quadratic programming approaches for the general graph partitioning problem

The graph partitioning problem is to partition the vertex set of a graph into a number of nonempty subsets so that the total weight of edges connecting distinct subsets is minimized. Previous research requires the input of cardinalities of subsets or the number of subsets for equipartition. In this paper, the problem is formulated as a zero-one quadratic programming problem without the input of cardinalities. We also present three equivalent zero-one linear integer programming reformulations. Because of its importance in data biclustering, the bipartite graph partitioning is also studied. Several new methods to determine the number of subsets and the cardinalities are presented for practical applications. In addition, hierarchy partitioning and partitioning of bipartite graphs without reordering one vertex set, are studied.

Recursively Accelerated Multilevel Aggregation for Markov Chains

A recursive acceleration method is proposed for multiplicative multilevel aggregation algorithms that calculate the stationary probability vector of large, sparse, and irreducible Markov chains. Pairs of consecutive iterates at all branches and levels of a multigrid W cycle with simple, nonoverlapping aggregation are recombined to produce improved iterates at those levels. This is achieved by solving quadratic programming problems with inequality constraints: the linear combination of the two iterates is sought that has a minimal two-norm residual, under the constraint that all vector components are nonnegative. It is shown how the two-dimensional quadratic programming problems can be solved explicitly in an efficient way. The method is further enhanced by windowed top-level acceleration of the W cycles using the same constrained quadratic programming approach. Recursive acceleration is an attractive alternative to smoothing the restriction and interpolation operators, since the operator complexity is better controlled and the probabilistic interpretation of coarse-level operators is maintained on all levels. Numerical results are presented showing that the resulting recursively accelerated multilevel aggregation cycles for Markov chains, combined with top-level acceleration, converge significantly faster than W cycles and lead to close-to-linear computational complexity for challenging test problems.

Calibration of local volatility using the local and implied instantaneous variance

We document the calibration of the local volatility in terms of local and implied instantaneous variances; we first explore the theoretical properties of the method for a particular class of volatilities. We confirm the theoretical results through a numerical procedure which uses a Gauss-Newton style approximation of the Hessian in the framework of a sequential quadratic programming (SQP) approach. The procedure performs well on benchmarks from the literature and on FOREX data.

Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach.

Tourism forecast combination using the CUSUM technique

Forecast combination in tourism has emerged as an important research area due to its relevance to tourism decision making. This paper further investigates the impact of forecast combination on forecast accuracy by applying a quadratic programming approach to determine the combination weights for individual forecasts. In particular, we introduce three novel ideas which have not been found in previous tourism forecasting studies. First, we introduce a quality control technique, CUSUM, to determine the time for updating the weights. Next, we develop a hybrid method (using quadratic programming) to combine the forecasts to reduce forecasting errors. Thirdly, we investigate whether different performance measures yield different results. Thus, instead of comparing different weighting methods using only one performance measure, we introduce several indicators for performance comparisons. The empirical results suggest that the controlled weighting method both saves time in updating the combination weights and improves the overall performance of the combined forecasts. The method is also easy-to-implement and should be used to improve forecasting accuracy in practice.

Optimal Design of Nonlinear-Phase FIR Filters With Prescribed Phase Error

Constrained least-squares design and constrained Chebyshev design of one- and two-dimensional nonlinear-phase FIR filters with prescribed phase error are considered in this paper by a unified semi-infinite positive-definite quadratic programming approach. In order to obtain unique optimal solutions, we propose to impose constraints on the complex approximation error and the phase error. By introducing a sigmoid phase-error constraint bound function, the group-delay error can be greatly reduced. A Goldfarb-Idnani based algorithm is presented to solve the semi-infinite positive-definite quadratic program resulting from the constrained least-squares design problem, and then applied after some modifications to the constrained Chebyshev design problem, which is proved in this paper to be equivalent also to a semi-infinite positive-definite quadratic program. Through design examples, the proposed method is compared with several existing methods. Simulation results demonstrate the effectiveness and efficiency of the proposed method.

FSWM: A hybrid fuzzy-stochastic water-management model for agricultural sustainability under uncertainty

A hybrid fuzzy-stochastic water-management (FSWM) model is developed for agricultural sustainability under uncertainty, based on advancement of a multistage fuzzy-stochastic quadratic programming (MFSQP) approach. In MFSQP, uncertainties presented in terms of fuzziness and randomness can be incorporated within a multilayer scenario tree, such that revised decisions are permitted in each time period based on the realized values of the uncertain events. Moreover, fuzzy quadratic terms are used in the objective function to minimize the variation of satisfaction degrees among the constraints; it allows an increased flexibility in controlling the system risk in the optimization process. Results of the case study indicate that useful solutions for the planning of agricultural water management have been obtained. In the FSWM model, a number of policies for agricultural water supply are conducted. The results obtained can help decision makers to identify desired water-allocation schemes for agricultural sustainability under uncertainty, particularly when limited water resources are available for multiple competing users.

An integrated perturbation analysis and Sequential Quadratic Programming approach for Model Predictive Control

Computationally efficient algorithms are critical in making Model Predictive Control (MPC) applicable to broader classes of systems with fast dynamics and limited computational resources. In this paper, we propose an integrated formulation of Perturbation Analysis and Sequential Quadratic Programming (InPA-SQP) to address the constrained optimal control problems. The proposed algorithm combines the complementary features of perturbation analysis and SQP in a single unified framework, thereby leading to improved computational efficiency and convergence property. A numerical example is reported to illustrate the proposed method and its computational effectiveness.

An improved hybrid global optimization method for protein tertiary structure prediction

First principles approaches to the protein structure prediction problem must search through an enormous conformational space to identify low-energy, near-native structures. In this paper, we describe the formulation of the tertiary structure prediction problem as a nonlinear constrained minimization problem, where the goal is to minimize the energy of a protein conformation subject to constraints on torsion angles and interatomic distances. The core of the proposed algorithm is a hybrid global optimization method that combines the benefits of the αBB deterministic global optimization approach with conformational space annealing. These global optimization techniques employ a local minimization strategy that combines torsion angle dynamics and rotamer optimization to identify and improve the selection of initial conformations and then applies a sequential quadratic programming approach to further minimize the energy of the protein conformations subject to constraints. The proposed algorithm demonstrates the ability to identify both lower energy protein structures, as well as larger ensembles of low-energy conformations.

A rolling-horizon quadratic-programming approach to the signal control problem in large-scale congested urban road networks

The paper investigates the efficiency of a recently developed signal control methodology, which offers a computationally feasible technique for real-time network-wide signal control in large-scale urban traffic networks and is applicable also under congested traffic conditions. In this methodology, the traffic flow process is modeled by use of the store-and-forward modeling paradigm, and the problem of network-wide signal control (including all constraints) is formulated as a quadratic-programming problem that aims at minimizing and balancing the link queues so as to minimize the risk of queue spillback. For the application of the proposed methodology in real time, the corresponding optimization algorithm is embedded in a rolling-horizon (model-predictive) control scheme. The control strategy’s efficiency and real-time feasibility is demonstrated and compared with the Linear-Quadratic approach taken by the signal control strategy TUC (Traffic-responsive Urban Control) as well as with optimized fixed-control settings via their simulation-based application to the road network of the city centre of Chania, Greece, under a number of different demand scenarios. The comparative evaluation is based on various criteria and tools including the recently proposed fundamental diagram for urban network traffic.

Piecewise regression for fuzzy input–output data with automatic change-point detection by quadratic programming

To handle the large variation issues in fuzzy input–output data, the proposed quadratic programming (QP) method uses a piecewise approach to simultaneously generate the possibility and necessity models, as well as the change-points. According to Tanaka and Lee [H. Tanaka, H. Lee, Interval regression analysis by quadratic programming approach, IEEE Transactions on Fuzzy Systems 6 (1998) 473–481], the QP approach gives more diversely spread coefficients than linear programming (LP) does. However, their approach only deals with crisp input and fuzzy output data. Moreover, their method is weak in handling fluctuating data. So far, no method has been developed to cope with the large variation problems in fuzzy input–output data. Hence, we propose a piecewise regression for fuzzy input–output data with a QP approach. There are three advantages in our method. First, the QP technique gives a more diversely spread coefficient than does a linear programming technique. Second, the piecewise approach is used to detect the change-points in the estimated model automatically, and handle the large variation data such as outliers well. Third, the possibility and necessity models with better fitness in data processing are obtained at the same time. Two examples are presented to demonstrate the merits of the proposed method.

On the accurate prediction of interfacial micro-slip in frictional joints using distributed dislocations and quadratic programming techniques

Relative displacement between pre-stressed and frictionally interlocked components can play a major role in the failure of mechanical assemblies. The undesired relative motion between the mating parts constituting the coupling may be the result of the accumulation of interfacial micro-slip along a preferred direction. Classical approaches for the design of these systems are based on macroscopic criteria, where potentially severe localised stress conditions giving rise to micro-slip are not considered. A quadratic programming approach which enables to resolve interfacial micro-slip adopting the distributed dislocation technique is proposed here to overcome the limitation of existing formulations.

A FUZZY DECISION‐MAKING APPROACH FOR PORTFOLIO MANAGEMENT WITH DIRECT REAL ESTATE INVESTMENT

This study incorporated expert knowledge into the classical quadratic programming approach, i.e., Modern Portfolio Theory (MPT), through fuzzy set theory; in obtaining portfolio return optimization involving direct real estate investment. Two fuzzy mathematical programming models were uniquely specified and estimated in this study, namely, Zimmer‐mann's (2001) fuzzy tactical asset allocation (FTAA) flexible programming model and Ramik and Rimanek's (1985) FTAA robust programming model. These approaches try to overcome the drawbacks of traditional asset allocation models by including expert adjustment in the presence of imprecise information. The findings suggest that the fuzzy tactical asset allocation (FTAA Flexible Model), with the inclusion of expert judgments which contain information usually not found in historical data, is able to produce a portfolio just as efficient as traditional asset allocation models while minimizing the potential issues due to imprecision and vagueness of information. Meanwhile, the FTAA Robust Model proffers a more evenly‐distributed, yet with higher risks and lower returns, portfolio. Aside from the lack of emphasis on portfolio risks minimization, one reason attributed to such anomaly is the low level of returns of high‐risk stocks that are not selected by MPT and FTAA Flexible Models. It results in a unique situation where portfolio diversification does not necessarily guarantee an efficient investment decision. Santruka Šis tyrimas itraukia ekspertines žinias i klasikine kvadratinio programavimo metodika, pavyzdžiui, moderniaja portfelio valdymo teorija, per neapibrežtuju aibiu teorija, siekiant optimizuoti portfelio graža, apimant tiesiogines nekilnojamojo turto investicijas. Šiame tyrime išsamiai aprašomi ir ivertinami du neapibrežtojo matematinio programavimo modeliai. Tai Zimmermann (2001) neapibrežtasis aktyvu paskirstymo lankstusis programavimo modelis ir Ramik bei Rimanek (1985) neapibrežtasis aktyvu paskirstymo robustinis programavimo modelis. Juos taikant bandoma pašalinti tradiciniu aktyvu paskirstymo metodu trūkumus itraukiant ekspertu siūlomus pakeitimus nesant tikslios informacijos. Nustatyta, kad neapibrežtasis aktyvu paskirstymas (neapibrežtasis aktyvu paskirstymo lankstusis programavimo modelis) kartu su ekspertu vertinimais, paprastai apimančiais informacija, kurios negalima rasti tarp istoriniu duomenu, leidžia sudaryti toki pati efektyvu portfeli, kaip ir tradiciniai aktyvu paskirstymo modeliai, tačiau minimizuojant potencialius nesutarimus, kuriu atsiranda del netikslios ir neapibrežtos informacijos. Neapibrežtasis aktyvu paskirstymo robustinis programavimo modelis siūlo tolygiau paskirstyta, tačiau rizikingesni ir ne toki pelninga portfeli. Be portfelio rizikos minimizavimo trūkumo, dar viena priežastis, priskiriama prie šios anomalijos, yra maža dideles rizikos akciju graža, kuri nera pasirenkama moderniojoje portfelio valdymo teorijoje ir neapibrežtuju aktyvu paskirstymo lanksčiuosiuose programavimo modeliuose. Kaip rezultatas gaunama unikali situacija, kai portfelio diversifikavimas nebūtinai garantuoja efektyvu investavimo sprendima.

A Quadratic Programming Approach to Blind Equalization and Signal Separation

Blind equalization and signal separation are two well-established signal processing problems. In this paper, we present a quadratic programming algorithm for fast blind equalization and signal separation. By introducing a special non-mean-square error (MSE) objective function, we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem. Based on a clear geometric interpretation and a formal proof, we show that a perfect equalization solution is obtained at every local optimum of the quadratic program. Because blind source separation is, by nature and mathematically, a closely related problem, we also generalize the algorithm for blind signal separation. We show that by enforcing source orthogonalization through successive processing, the quadratic programming approach can be applied effectively. Moreover, the quadratic program is easily extendible to incorporate additional practical conditions, such as jamming suppression constraints. We also provide evidence of good performance through computer simulations.

Alignment of Confocal Scanning Laser Ophthalmoscopy Photoreceptor Images at Different Polarizations Using Complex Phase Relationships

A polarimetric technique for enhancing fundus images was recently introduced , where confocal scanning laser ophthalmoscopy (CSLO) images are acquired under differing incoming polarization states, and spatially resolved Mueller images are constructed based on the images. An important stage in this technique is the alignment of CSLO images acquired under differing polarization states. This has proven to be particularly difficult when dealing with photoreceptor images, which are characterized by poor SNRs and intensity inhomogeneities due to polarization properties. In this paper, an automated approach to aligning CSLO photoreceptor images acquired under differing polarization states is presented. A novel energy functional based on complex phase relationships is introduced that is invariant to polarization and scale, as well as robust to noise and highly sensitive to photoreceptor structural characteristics. A sequential quadratic programming approach is employed to determine the optimal alignment between the photoreceptor images by minimizing the proposed energy functional. The method has been tested on CSLO fish photoreceptor images acquired under differing polarization states and evaluated based on alignment accuracy. The results demonstrate that the proposed method outperforms existing techniques used for aligning CSLO images, with lower mean alignment error for all test cases.

An Iterative Algorithm to Minimize Loss Energy in Mobile Robot

As a consequence of physical constraints and of dynamical nonlinearities of the limbs, optimal control problems involving mobile robots with legs are generally difficult ones. Minimum energy problems subject to both equality and inequality constraints are generally intricate ones to be solved using classical methods. In this paper we propose and prove the convergence of a new algorithm to solve a minimum energy problem in motion of mobile robots using a Quadratic Programming approach. The results of the application of the algorithm to a robotic platform are shown.

Placement of Synchronized Measurements for Power System Observability

This paper presents a method for the use of synchronized measurements for complete observability of a power system. The placement of phasor measurement units (PMUs), utilizing time-synchronized measurements of voltage and current phasors, is studied in this paper. An integer quadratic programming approach is used to minimize the total number of PMUs required, and to maximize the measurement redundancy at the power system buses. Existing conventional measurements can also be accommodated in the proposed PMU placement method. Complete observability of the system is ensured under normal operating conditions as well as under the outage of a single transmission line or a single PMU. Simulation results on the IEEE 14-bus, 30-bus, 57-bus, and 118-bus test systems as well as on a 298-bus test system are presented in this paper.

A quadratic programming approach to image labelling

Image labelling tasks are usually formulated within the framework of discrete Markov random fields where the optimal labels are recovered by extremising a discrete energy function. The authors present an alternative continuous relaxation approach to image labelling, which makes use of a quadratic cost function over the class labels. The cost function to be minimised is convex and its discrete version is equivalent up to a constant additive factor to the target function used in discrete MRF approaches. Moreover, its corresponding Hessian matrix is given by the graph Laplacian of the adjacency matrix. Therefore the optimisation of the cost function is governed by the pairwise interactions between pixels in the local neighbourhood. This leads to a sparse Hessian matrix for which the global minimum of the continuous relaxation problem can be efficiently found by solving a system of linear equations using the Cholesky factorisation. The authors elaborate on the links between the method and other techniques elsewhere in the literature and provide results on synthetic and real-world imagery. The authors also provide a comparison with competing approaches.

Duality-based algorithms for total-variation-regularized image restoration

Image restoration models based on total variation (TV) have become popular since their introduction by Rudin, Osher, and Fatemi (ROF) in 1992. The dual formulation of this model has a quadratic objective with separable constraints, making projections onto the feasible set easy to compute. This paper proposes application of gradient projection (GP) algorithms to the dual formulation. We test variants of GP with different step length selection and line search strategies, including techniques based on the Barzilai-Borwein method. Global convergence can in some cases be proved by appealing to existing theory. We also propose a sequential quadratic programming (SQP) approach that takes account of the curvature of the boundary of the dual feasible set. Computational experiments show that the proposed approaches perform well in a wide range of applications and that some are significantly faster than previously proposed methods, particularly when only modest accuracy in the solution is required.