Search results for "49J40"

showing 4 items of 4 documents

A Mountain Pass Theorem for a Suitable Class of Functions

2009

Class (set theory)geographyPure mathematicsgeography.geographical_feature_categorycritical pointsGeneral Mathematicsthree solutions58E30two-point boundary value problemPalais-Smale conditionmountain pass34B1558E05A mountain pass theoremCombinatoricsPalais–Smale compactness conditionSettore MAT/05 - Analisi MatematicaMountain pass theoremMountain pass49J4047J30Mathematics
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A differential equation approach to implicit sweeping processes

2019

International audience; In this paper, we study an implicit version of the sweeping process. Based on methods of convex analysis, we prove the equivalence of the implicit sweeping process with a differential equation, which enables us to show the existence and uniqueness of the solution to the implicit sweeping process in a very general framework. Moreover, this equivalence allows us to give a characterization of nonsmooth Lyapunov pairs and invariance for implicit sweeping processes. The results of the paper are illustrated with two applications to quasistatic evolution variational inequalities and electrical circuits.

Lyapunov functionDifferential equation01 natural scienceslaw.inventionsymbols.namesakeEvolution variational inequalitylawApplied mathematicsUniqueness0101 mathematicsEquivalence (formal languages)[MATH]Mathematics [math]MathematicsConvex analysisApplied Mathematics010102 general mathematicsNonsmooth Lyapunov pairs010101 applied mathematicsregularizationMSC: 49J40 47J20 47J22 34G25 58E35 37L45Electrical networkVariational inequalitysymbolsMoreau's sweeping processAnalysisQuasistatic process
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Weak and strong convergence of an inertial proximal method for solving bilevel monotone equilibrium problems

2022

In this paper, we introduce an inertial proximal method for solving a bilevel problem involving two monotone equilibrium bifunctions in Hilbert spaces. Under suitable conditions and without any restrictive assumption on the trajectories, the weak and strong convergence of the sequence generated by the iterative method are established. Two particular cases illustrating the proposed method are thereafter discussed with respect to hierarchical minimization problems and equilibrium problems under saddle point constraint. Furthermore, a numerical example is given to demonstrate the implementability of our algorithm. The algorithm and its convergence results improve and develop previous results i…

Weak and strong convergenceBilevel Equilibrium problemsOptimization and Control (math.OC)G.1.6Equilibrium Fitzpatrick transformFOS: MathematicsProximal algorithm90C33 49J40 46N10 65K15 65K10[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Monotone bifunctionsMathematics - Optimization and Control
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Shape optimization in contact problems based on penalization of the state inequality

1986

The paper deals with the approximation of optimal shape of elastic bodies, uni­laterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established. peerReviewed

msc:49M30msc:73k40frictionless plane contact [keyword]minimization of the total potential energy [keyword]msc:74M15linear-elastic sheet [keyword]rigid foundation [keyword]msc:74P99contact boundary curve [keyword]family of penalized state problems [keyword]existence [keyword]msc:49J40convergence [keyword]nonlinear programming problem [keyword]msc:73T05shape optimization [keyword]box constraints [keyword]msc:74S05linear equality constraint [keyword]msc:74A55linear inequality constraints [keyword]
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