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SENSITIVITY ANALYSIS IN CONVEX QUADRATIC OPTIMIZATION: INVARIANT SUPPORT SET INTERVAL
, 2004
"... In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the r ..."
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Cited by 9 (4 self)
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In sensitivity analysis one wants to know how the problem and the optimal solutions change under the variation of the input data. We consider the case when variation happens in the right hand side of the constraints and/or in the linear term of the objective function. We are interested to find the range of the parameter variation in Convex Quadratic Optimization (CQO) problems where the support set of a given primal optimal solution remains invariant. This question has been first raised in Linear Optimization (LO) and known as Type II (so called Support Set Invariancy) sensitivity analysis. We present computable auxiliary problems to identify the range of parameter variation in support set invariancy sensitivity analysis for CQO. It should be mentioned that all given auxiliary problems are LO problems and can be solved by an interior point method in polynomial time. We also highlight the differences between characteristics of support set invariancy sensitivity analysis for LO and CQO.
Title: BiParametric Convex Quadratic Optimization Authors:
"... In this paper we consider the Convex Quadratic Optimization problem with simultaneous perturbation in the righthandside of the constraints and the linear term of the objective function with different parameters. The regions with invariant optimal partitions are investigated as well as the behavior ..."
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In this paper we consider the Convex Quadratic Optimization problem with simultaneous perturbation in the righthandside of the constraints and the linear term of the objective function with different parameters. The regions with invariant optimal partitions are investigated as well as the behavior of the optimal value function on the regions. We show that identifying these regions can be done in polynomial time in the output size. An algorithm for identifying all invariancy regions is presented. Some implementation details, as well as a numerical example are discussed.
Parametric and Multiobjective Optimization with Applications in Finance
, 2010
"... In this thesis parametric analysis for conic quadratic optimization problems is studied. In parametric analysis, which is often referred to as parametric optimization or parametric programming, a perturbation parameter is introduced into the optimization problem, which means that the coefficients in ..."
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In this thesis parametric analysis for conic quadratic optimization problems is studied. In parametric analysis, which is often referred to as parametric optimization or parametric programming, a perturbation parameter is introduced into the optimization problem, which means that the coefficients in the objective function of the problem and in the righthandside of the constraints are perturbed. First, we describe linear, convex quadratic and second order cone optimization problems and their parametric versions. Second, the theory for finding solutions of the parametric problems is developed. We also present algorithms for solving such problems. Third, we demonstrate how to use parametric optimization techniques to solve multiobjective optimization problems and compute Pareto efficient surfaces. We implement our novel algorithm for biparametric quadratic optimization. It utilizes existing solvers to solve auxiliary problems. We present numerical results produced by our parametric optimization package on a number of practical