Quadratic Programming as an Extension of Classical Quadratic Maximization

Theil, Henri; Panne, C. van de

doi:10.1007/978-94-011-2410-2_11

Cited by 30 publications

(8 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Several numerical methods are available for solving constrained optimization problems via the method of Lagrange multipliers, but many are restricted to small or medium-sized problems (e.g., s has fewer than 1000 elements). These include the method of Theil and Van de Panne (Theil and Panne, 1960;Snyman, 2005, Chap. 3.4) and the active set method (e.g., Gill et al, 1981, or Antoniou andLu, 2007, Chap.…”

Section: Lagrange Multipliers and The Trust Region Algorithmmentioning

confidence: 99%

Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions

2014

View full text Add to dashboard Cite

Abstract. Many inverse problems in the atmospheric sciences involve parameters with known physical constraints. Examples include nonnegativity (e.g., emissions of some urban air pollutants) or upward limits implied by reaction or solubility constants. However, probabilistic inverse modeling approaches based on Gaussian assumptions cannot incorporate such bounds and thus often produce unrealistic results. The atmospheric literature lacks consensus on the best means to overcome this problem, and existing atmospheric studies rely on a limited number of the possible methods with little examination of the relative merits of each. This paper investigates the applicability of several approaches to bounded inverse problems. A common method of data transformations is found to unrealistically skew estimates for the examined example application. The method of Lagrange multipliers and two Markov chain Monte Carlo (MCMC) methods yield more realistic and accurate results. In general, the examined MCMC approaches produce the most realistic result but can require substantial computational time. Lagrange multipliers offer an appealing option for large, computationally intensive problems when exact uncertainty bounds are less central to the analysis. A synthetic data inversion of US anthropogenic methane emissions illustrates the strengths and weaknesses of each approach.

show abstract

Section: Lagrange Multipliers and The Trust Region Algorithmmentioning

confidence: 99%

Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions

2014

View full text Add to dashboard Cite

show abstract

“…The first n equations in ( 5 ) are, in fact, the marginal utility functions of n assets (see Sharpe 14). The physical meanings of the lagrangian muItipliers are clear here.…”

Section: Portfolio Optimizationmentioning

confidence: 99%

Quadratic programming for portfolio optimization

Ho¹

1992

Appl. Stochastic Models Data Anal.

View full text Add to dashboard Cite

SUMMARYPortfolio optimization is a procedure for generating a portfolio composition which yields the highest return for a given level of risk or a minimum risk for given level of return. The problem can be formulated as a quadratic programming problem. We shall present a new and efticient optimization procedure taking advantage of the special structure of the portfolio selection problem. An example of its application to the traditional mean-variance method will be shown. Formulation o f the procedure shows that the solution of the problem is vector intensive and fits well with the advanced architecture of recent computers, namely the vector processor.

show abstract

“…Some of them are extensions of the simplex method and others are based on different principles. In the conversance, a great number of methods (Wolf 1 , Beale 2 , Frank and Wolf 3 , Shetty 4 , Lemke 5 , Best and Ritter 6 , Theil and van de Panne 7 , Boot 8 , Fletcher 9 , Swarup 10 , Gupta and Sharma 11 , Moraru 12,13 , Jensen and King 14 , Bazaraa, Sherali and Shetty 1 5 ) are designed to solve QP problems in a finite number of steps. Among them, Wolf's method 1 , Swarup's simplex method 10 and Gupta and Sharma's method 11 are more popular than the other methods.…”

Section: Introductionmentioning

confidence: 99%

A Proposed Technique for Solving Quasi-Concave Quadratic Programming Problems with Bounded Variables by Objective Separable Method

Asadujjaman

Hasan

2016

Dhaka Univ. J. Sci.

View full text Add to dashboard Cite

In this paper, a new method namely, objective separable method based on Linear Programming with Bounded Variables Algorithm is proposed for finding an optimal solution to a Quasi-Concave Quadratic Programming Problems with Bounded Variables in which the objective function involves the product of two indefinite factorized linear functions and the constraint functions are in the form of linear inequalities. For developing this method, we use programming language MATHEMATICA. We also illustrate numerical examples to demonstrate our method.Dhaka Univ. J. Sci. 64(1): 51-58, 2016 (January)

show abstract

Quadratic Programming as an Extension of Classical Quadratic Maximization

Cited by 30 publications

References 5 publications

Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions

Atmospheric inverse modeling with known physical bounds: an example from trace gas emissions

Quadratic programming for portfolio optimization

A Proposed Technique for Solving Quasi-Concave Quadratic Programming Problems with Bounded Variables by Objective Separable Method

Contact Info

Product

Resources

About