Constraint qualifications for convex optimization without convexity of constraints : New connections and applications to best approximation

Chiêu, Nguyễn Huy; Jeyakumar, V.; Li, Guoyin; Mohebi, H.

doi:10.1016/j.ejor.2017.07.038

Cited by 18 publications

(11 citation statements)

References 14 publications

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“…In the infinite-dimensional framework, when T is finite, we show in Theorem 9 that if all the active functions, except perhaps one of them, namely f k0 , are continuous at a common point in dom f , then (2) \partialf (x) = co The last formula extends well-known results in [25] and [30]. More precisely, the following result of [30] requires that all the functions f k , k \in T, except perhaps one of them (not only the active ones as in our formula (2)) are continuous at some point in dom f :…”

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confidence: 93%

“…Moreover, a variant Downloaded 04/30 /19 to 193.145.230.254. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php of (4) was shown in [16,Theorem 3.1] to be necessary for the validity of formula (2) in the Banach setting. In contrast to some results in [6], a feature of the present paper is that we succeed in removing this condition, increasing in this way the validity of Theorems 1 and 4 in [6].…”

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confidence: 99%

“…since for t \in \widehat T (\= x) one has \partialf t (\= x) + N dom ft (\= x) = \partialf t (\= x). It is worth mentioning that alternative KKT conditions exist in the literature, obtained via many different approaches: approximate subdifferentials of the data functions [3,13], exact subdifferentials at close points [28], asymptotic KKT conditions [19] for linear semi-infinite programming, Farkas--Minkowski-type closedness criteria [8] in convex semi-infinite optimization, and strong CHIP-like qualifications (where CHIP stands for conical hull intersection property) for convex optimization with not necessarily convex C 1 -constraints [2] (see also [9] for locally Lipschitz constraints), among others. We also refer the reader to [32] and references therein for KKT conditions in the framework of subsmooth semi-infinite optimization, and to [10] for analysis of the relationships among KKT rules and Lagrangian dualities.…”

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confidence: 99%

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Moreau--Rockafellar-Type Formulas for the Subdifferential of the Supremum Function

Corrêa¹,

Hantoute²,

Cerdá³

2019

SIAM J. Optim.

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We characterize the subdifferential of the supremum function of finitely and infinitely indexed families of convex functions. The main contribution of this paper consists of providing formulas for such a subdifferential under weak continuity assumptions. The resulting formulas are given in terms of the exact subdifferential of the data functions at the reference point, and not at nearby points as in [Valadier, C. R. Math. Acad. Sci. Paris, 268 (1969), pp. 39-42]. We also derive new Fritz John-and KKT-type optimality conditions for semi-infinite convex optimization, omitting the continuity/closedness assumptions in [Dinh et al., ESAIM Control Optim. Calc. Var., 13 (2007), pp. 580-597]. When the family of functions is finite, we use continuity conditions concerning only the active functions, and not all the data functions as in [Rockafellar,

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confidence: 93%

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confidence: 99%

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confidence: 99%

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Moreau--Rockafellar-Type Formulas for the Subdifferential of the Supremum Function

Corrêa¹,

Hantoute²,

Cerdá³

2019

SIAM J. Optim.

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“…Also, using a version of the strong CHIP, we give a constraint qualification which is necessary for optimality of the problem (P). Finally, we present necessary and sufficient conditions for optimality of the problem (P), extending known results in the finite dimensional case (see [4,8,11] and other references therein).…”

Section: Introductionmentioning

confidence: 60%

Optimality conditions for nonconvex problems over nearly convex feasible sets

Ghafari

Mohebi

2021

Arab. J. Math.

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In this paper, we study the optimization problem (P) of minimizing a convex function over a constraint set with nonconvex constraint functions. We do this by given new characterizations of Robinson’s constraint qualification, which reduces to the combination of generalized Slater’s condition and generalized sharpened nondegeneracy condition for nonconvex programming problems with nearly convex feasible sets at a reference point. Next, using a version of the strong CHIP, we present a constraint qualification which is necessary for optimality of the problem (P). Finally, using new characterizations of Robinson’s constraint qualification, we give necessary and sufficient conditions for optimality of the problem (P).

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“…Furthermore, with one location matrix L m ×88 , the calculation of

normalΔ k_{{normalF}_{1}} ((), u)

normalΔ k_{{normalF}_{2}} ((), u)

, …,

normalΔ k_{{normalF}_{88}} ((), u)

is to minimize the following expression to zero:

minimize {|L_{m \times 88} (R_{88 \times 88} {([], \begin{array}{l} normalΔ k_{F_{1}} ((), u) \\ normalΔ k_{F_{2}} ((), u) \\ \dots \\ normalΔ k_{F_{88}} ((), u) \end{array})}_{88 \times 1}) - {([], \begin{array}{l} normalΔ k_{DA, n_{1}} ((), u) \\ normalΔ k_{DA, n_{2}} ((), u) \\ \dots \\ normalΔ k_{DA, n_{m}} ((), u) \end{array})}_{m \times 1}|}_{2},

where the role of location matrix L m ×88 is to specially select the AVSLD s at the installed locations n 1 , n 2 , …, n m . Equation can be solved using the convex optimization method …”

Section: Mechanical Modeling Analysismentioning

confidence: 99%

Localization and quantification of partial cable damage in the long-span cable-stayed bridge using the abnormal variation of temperature-induced girder deflection

Gao-xin

2018

Struct Control Health Monit

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The cable damage is one serious problem to endanger the bridge safety. Considering that current methods of estimating cable damage still have some shortcomings during their application, this paper introduced one new method to localize and quantify the partial cable damage using the abnormal variation of temperature-induced girder deflection caused by cable damage. First, the monitoring correlation between girder deflection and uniform temperature is analyzed using the monitoring temperature and deflection data. Second, the abnormal variations of temperature-induced girder deflection and cable force are deeply researched through finite element simulation. Third, the correlation between girder deflection and cable force is mechanically modeled, and furthermore, the method of localizing and quantifying partial cable damage is put forward. Specifically, the envelope curve is created to localize the broken stay cable, and the damage indicator is used to quantify the partial damage in the broken stay cable. Furthermore, the influence of two parameters (viz., the environmental noise and sensor quantity) on the localization and quantification accuracy is discussed. Overall, the results show that the proposed method is feasible to localize and quantify the partial cable damage. KEYWORDS broken stay cable, cable-stayed bridge, localization and quantification, temperature-induced cable force, temperature-induced girder deflection

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Constraint qualifications for convex optimization without convexity of constraints : New connections and applications to best approximation

Cited by 18 publications

References 14 publications

Moreau--Rockafellar-Type Formulas for the Subdifferential of the Supremum Function

Moreau--Rockafellar-Type Formulas for the Subdifferential of the Supremum Function

Optimality conditions for nonconvex problems over nearly convex feasible sets

Localization and quantification of partial cable damage in the long-span cable-stayed bridge using the abnormal variation of temperature-induced girder deflection

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