Quadratic programming method in numerical simulation of metal forming process

Applications of linear programming in analyzing and evaluating various policies related to agriculture have been numerous. The use of quadratic programming is relatively less common. The computational aspects of the problem present an important limitation on the use of quadratic programming when size of the model used is relatively large. In the present study, separable programming was applied to solve a quadratic programming model of U.S. agriculture. The quadratic objective function of the model was transformed into a separable function using eigenvalues and eigenvectors of the demand matrix. The quadratic programming model is formulated in such a way that number of constraints in the model is relatively small which facilitates application of separable programming to a broad spectrum of problems;The quadratic programming model is used to analyze the impact of alternative energy price and supply situations on the crop production sector of U.S. agriculture. In recent years, continuous rise in energy prices and prospects of reduction in fossil fuel-based energy supply are having numerous effects on the use of energy in all sectors of the economy and development of competing energy sources. In the present study, impact of alternative energy situations is analyzed on a number of variables related to agriculture which may be listed as follows: land, water, nitrogen and energy use in farming, regional crop production patterns, methods of farming, resource and output prices, energy and nonenergy related expenses in crop production, farm income and consumer expenditures on farm products at farm level;With increased energy prices, reduction in the use of inputs such as water and commercial fertilizer nitrogen which require energy was observed similarly. Reduction in irrigated farming and increase in acreages under minimum tillage were also observed as means of accomplishing reductions in energy use. But the decrease in energy used in farm production was very small relative to the increase in energy prices. Crop prices at farm-level, total cost of crop production, consumer expenditures at farm level and net farm income all increase due to increased energy prices;When energy supplies are reduced, the main results are similar to those observed when the energy prices increased. Regional level reduction in energy supply, rather than the national level reduction causes the nonenergy related cost of production to increase under the former alternative relative to the latter.

This paper reviews some advances and applications in mathematical programming method for numerical modeling of elastic-plastic contact problems. Emphases are on the parametric variational principle and quadratic programming method used for analysis of elastic-plastic contact problems with isotropic/orthotropic friction law. The contact problem with friction between two elastic-plastic Cosserat bodies is treated in the same way as that in the conventional plastic analysis. There is no available rule for choosing a reasonable value of the penalty factors for simulation of the contact problems of Cosserat materials, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. Two numerical examples are presented to show the efficiency of the model and algorithm presented.

This paper presents a reactive power optimization model that is based on successive quadratic programming (SQP) methods. Mathematical formulation and unified algorithm suppose different objective functions (OF) of reactive power optimization, depending on type and purposes of current reactive power control or planning problem. A bicriterion reactive power optimization model, that represents compromise between economical and security objective functions, is proposed. An efficient algorithm for approximation of initial problem by quadratic programming problem is described. The quadratic programming problem (QP) is solved on the basis of the Newton type quadratic programming method. A modified successive quadratic programming method was developed, that provides reliable convergence of the SQP method.

The aim of this paper is to present a review on the state-of-the-art related to quadratic programming (QP) according to the methodology of Kitchenham and Charter. Our review was motivated from four questions: Q1: In what areas are quadratic programming models used? Q2: What optimization methods are used to solve quadratic programming problems? Q3: What optimization methods or algorithms have been used for portfolio selection? Q4: What optimization methods or algorithms solve quasiconvex quadratic problems? We obtain very interesting results on QP and discovered a new line of research for future investigations.KeywordsQuadratic programmingOptimization methodsQuasiconvex quadratic problemsPortfolio selection problems

Complexity and convergence certification of a block principal pivoting method for box-constrained quadratic programs

This paper investigates identification of parameter and measurement errors in the power network model. A mixed integer quadratic programming (MIQP) model is proposed in this paper to precisely identify multiple parameter and measurement errors. In the proposed MIQP model, erroneous parameters and measurements are involved with penalty factor in the aim of minimizing weighted least-squares (WLS) objective function. The proposed method has the desired property of accurate identification with avoiding over identification in the meantime. Parameter and measurement errors can also be distinguished simultaneously in MIQP model. All these features are verified via simulations that are carried out on IEEE 14-bus system.

One particularly known problem that confronts the farmer is that of determining optimal crop combinations for an intercropping scheme. This work therefore sets out to develop a model which determines optimally a crop combination that will yield maximum profit when interactive effects are present. A quadratic programming model is developed herein for selecting such an optimal crop combination for the intercropping scheme. A numerical application of the model shows that the model is adequate for such purposes. Keywords: Quadratic Programming, Intercropping, Optimal Selection [Global Jnl Mathematical Sci Vol.2(1) 2003: 73-80]

Group decision making with incomplete intuitionistic preference relations based on quadratic programming models

In the field of farm management and in related multidisciplinary fields such as bio-economic farm modeling and hydro-economic regional modeling, much attention has recently been paid to positive mathematical programming (PMP), primarily because of its ability to exactly reproduce an observed set of endogenous input variables in the model (e.g., an observed land-use pattern for crop productions) as the result of optimization. In mathematical terms, PMP is an inverse problem of quadratic programming (QP), where the objective function is calibrated on the basis of the Kuhn-Tucker conditions for the optimization of the QP model and of a linear programming model that is prepared for the calibration of parameters in the QP model. The two types of optimum conditions derived from the models are combined to obtain linear equations for the calibration of the QP model. However, as is often the case with inverse problems, the equations for the calibration are indefinite because the number of parameters to be calibrated surpasses the number of equations. As a result, various methods have been proposed to solve this so-called “ill-posed” problem. The main objectives of the present paper are to examine how the calibration methods developed in previous PMP models are related to one another and to propose practical procedures for determining which calibration method is the most appropriate from the viewpoint of sensitivity analyses. A simple conceptual framework is proposed to relate the previously developed calibration methods, and it is then applied to exemplify criteria for selecting a calibration method from the viewpoint of simulation results. A new direction in PMP-based farm modeling in which more feasible simulation results can be derived is also discussed.

Parametric variational principle and quadratic programming method for van der Waals force simulation of parallel and cross nanotubes

A new approach to secure economic power dispatch

Quadratic programs (QP), minimizations of quadratic objectives subject to linear inequality and equality constraints, are at the heart of algorithms across scientific domains. Applications include fundamental tasks in geometry processing, simulation, engineering, animation and finance where the accurate, reliable, efficient, and scalable solution of QP problems is critical. However, available QP algorithms generally provide either accuracy or scalability - but not both. Some algorithms reliably solve QP problems to high accuracy but work only for smaller-scale QP problems due to their reliance on dense matrix methods. Alternately, many other QP solvers scale well via sparse, efficient algorithms but cannot reliably deliver solutions at requested accuracies. Towards addressing the need for accurate and efficient QP solvers at scale, we develop NASOQ, a new, full-space QP algorithm that provides accurate, efficient, and scalable solutions for QP problems. To enable NASOQ we construct a new row modification method and fast implementation of LDL factorization for indefinite systems. Together they enable efficient updates and accurate solutions of the iteratively modified KKT systems required for accurate QP solves. While QP methods have been previously tested on large synthetic benchmarks, to test and compare NASOQ's suitability for real-world applications we collect here a new benchmark set comprising a wide range of graphics-related QPs across physical simulation, animation, and geometry processing tasks. We combine these problems with numerous pre-existing stress-test QP benchmarks to form, to our knowledge, the largest-scale test set of application-based QP problems currently available. Building off of our base NASOQ solver we then develop and test two NASOQ variants against best, state-of-the-art available QP libraries - both commercial and open-source. Our two NASOQ-based methods each solve respectively 98.8% and 99.5% of problems across a range of requested accuracies from 10 -3 to 10 -9 with average speedups ranging from 1.7× to 24.8× over fastest competing methods.

Two aggregate-function-based algorithms for analysis of 3D frictional contact by linear complementarity problem formulation

In this paper we study the problem of minimizing weighted earliness and tardiness on a single machine when all the jobs share the same due date. We propose two quadratic integer programming models for solving both cases of unrestricted and restricted due dates, an auxiliary model based on unconstrained quadratic integer programming and an algorithmic scheme for solving each instance, according to its size and characteristics, in the most efficient way. The scheme is tested on a set of well-known test problems. By combining the solutions of the three models we prove the optimality of the solutions obtained for most of the problems. For large instances, although optimality cannot be proved, we actually obtain optimal solutions for all the tested instances.

To improve the teaching practice effect of clothing major, this study applies the practical clothing design method to the teaching of clothing major to analyze the digital clothing design and establishes a convex quadratic conic programming model for a class of force optimization problems. Then, this study transforms the optimality condition of the problem into a new projection equation system, constructs a suitable constant coefficient matrix according to the characteristics of the equation system, and obtains an equivalent linear equation system. In addition, this study proposes a full Newton step projection algorithm to directly solve the convex quadratic conic programming. Through the results of the experimental research, it can be seen that the practical clothing design method has a good application in the teaching of clothing majors, and it can be applied in the practice of clothing teaching.