Numerical computation of the projection of a point onto a polyhedron

Arioli, Mario; Laratta, A.; Menchi, Ornella

doi:10.1007/bf00935003

Cited by 11 publications

(6 citation statements)

References 4 publications

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“…We now perturb the data of problem (1) /~= Ilbll ' ~=tlAIIIIx*ll ~1' ~-llwll Let A + be the pseudo inverse of A and K the condition number of A:…”

Section: * This Research Was Partially Supported By the Progetto Finamentioning

confidence: 99%

“…In this and in the following section we assume m<n and A of full rank. The solution x* of the problem min 89 2 (1) hTx=b is the least distance solution from w of the system Arx=b (2) (in this paper II'll denotes the Euclidean norm for vectors and the corresponding induced norm for matrices, and hi'lit denotes the Frobenius norm [4]). The solution x* of problem (1) can be written explicitly as [4] :…”

Section: Introductionmentioning

confidence: 99%

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Error analysis of an algorithm for solving an underdetermined linear system

Arioli

Laratta

1985

Numer. Math.

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“…We now perturb the data of problem (1) /~= Ilbll ' ~=tlAIIIIx*ll ~1' ~-llwll Let A + be the pseudo inverse of A and K the condition number of A:…”

Section: * This Research Was Partially Supported By the Progetto Finamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Error analysis of an algorithm for solving an underdetermined linear system

Arioli

Laratta

1985

Numer. Math.

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“…Obviously, problems (3) and (17) are not equivalent because there may exist vector critical points which are not (weakly) efficient solutions for (3). Nevertheless, by solving problem (17) we can obtain some approximation of the set of solutions to (3).…”

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confidence: 99%

“…Nevertheless, by solving problem (17) we can obtain some approximation of the set of solutions to (3).…”

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confidence: 99%

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A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone

Rahmo¹,

Studniarski²

2017

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We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with "roulette wheel" selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.

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