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The Lagrangian, constraint qualifications and economics
Mathematical Methods of Operations Research, 2022 AbstractConsidering constrained choice, practitioners and theorists frequently invoke a Lagrangian to generate optimality conditions. Regular use of that vehicle requires, however, some constraintqualification. Yet many economists go easy on the mathematics of that issue. Conversely, few mathematicians elaborate on the economics of the context. Thereby
Sjur Didrik Flåm, Jan-J. Rückmann
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New Constraint Qualifications with Second-Order Properties in Nonlinear Optimization
Journal of Optimization Theory and Applications, 2019 Gabriel Haeser +2 more
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Fractal and Fractional, 2021 In this paper, we establish Fritz John stationary conditions for nonsmooth, nonlinear, semidefinite, multiobjective programs with vanishing constraints in terms of convexificator and introduce generalized Cottle type and generalized Guignard type ...
Kin Keung Lai +4 more
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On duality for nonsmooth Lipschitz optimization problems [PDF]
Yugoslav Journal of Operations Research, 2009 We present some duality theorems for a non-smooth Lipschitz vector optimization problem. Under generalized invexity assumptions on the functions the duality theorems do not require constraint qualifications.
Preda Vasile +2 more
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Mathematics, 2021 In this paper, we consider a class of mathematical programs with switching constraints (MPSCs) where the objective involves a non-Lipschitz term. Due to the non-Lipschitz continuity of the objective function, the existing constraint qualifications for ...
Jinman Lv, Zhenhua Peng, Zhongping Wan
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Min–sup-type zero duality gap properties for DC composite optimization problem
Journal of Inequalities and Applications, 2019 In this paper, we present min–sup-type zero duality gap properties for DC composite optimization problem with conic constraints. Using properties of the subdifferentials of involved functions, we introduce some new constraint qualifications.
Li Ping Tian, Dong Hui Fang
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On implicit variables in optimization theory [PDF]
Journal of Nonsmooth Analysis and Optimization, 2021 Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel programming ...
Matúš Benko, Patrick Mehlitz
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Inertial Extragradient Methods for Solving Split Equilibrium Problems
Mathematics, 2021 This paper presents two inertial extragradient algorithms for finding a solution of split pseudomonotone equilibrium problems in the setting of real Hilbert spaces. The weak and strong convergence theorems of the introduced algorithms are presented under
Suthep Suantai +2 more
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Strong and Total Lagrange Dualities for Quasiconvex Programming
Journal of Applied Mathematics, 2014 We consider the strong and total Lagrange dualities for infinite quasiconvex optimization problems. By using the epigraphs of the z-quasi-conjugates and the Greenberg-Pierskalla subdifferential of these functions, we introduce some new constraint ...
Donghui Fang, XianFa Luo, Xianyun Wang
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On an exact penality result and new constraint qualifications for mathematical programs with vanishing constraints [PDF]
Yugoslav Journal of Operations Research, 2019 In this paper, we considered the mathematical programs with vanishing constraints or MPVC. We proved that an MPVC-tailored penalty function, introduced in [5], is still exact under a very weak and new constraint qualification.
Nath Triloki, Khare Abeka
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