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arxiv: 2607.02339 · v1 · pith:IQPC3OWDnew · submitted 2026-07-02 · 🧮 math.OC

Sensitivity Analysis and Robust Optimal Control for Coupled Evolution Inclusions with State-Dependent Maximal Monotone Operators

Jinsheng Du , Boris Mordukhovich , Shengda Zeng This is my paper

Pith reviewed 2026-07-03 08:18 UTC · model grok-4.3

classification 🧮 math.OC
keywords evolution inclusionsmaximal monotone operatorsoptimal controlrobust controlsensitivity analysisBolza problemparameter uncertainty
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The pith

For Bolza-type optimization over solutions of coupled evolution inclusions with state-dependent maximal monotone operators, optimal pairs exist, the value function is continuous, and the optimal-solution map is upper semicontinuous.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies a class of strongly coupled nonsmooth systems with a semilinear evolution inclusion and a differential inclusion governed by state-dependent maximal monotone operators. It first establishes well-posedness, compactness, and Painlevé-Kuratowski continuity of the parameterized solution map. Building on this, it proves existence of optimal pairs for Bolza-type optimization, continuity of the value function, and upper semicontinuity of the optimal-solution map. It further shows existence results for fixed-parameter optimal control, simultaneous control-parameter design, min-max robust control, and Hurwicz-type compromise control under parameter uncertainty.

Core claim

The parameterized solution map for these coupled systems has well-posedness, compactness, and Painlevé-Kuratowski continuity properties. For Bolza-type optimization over the solution set, optimal pairs exist, the value function has continuity properties, and the optimal-solution map is upper semicontinuous. Existence results hold for fixed-parameter optimal control, simultaneous control-parameter design, min-max robust control, and Hurwicz-type compromise control under parameter uncertainty.

What carries the argument

The parameterized solution map of the coupled semilinear evolution inclusion and differential inclusion with state-dependent maximal monotone operators, which carries the well-posedness and continuity properties used for all optimization results.

If this is right

  • Optimal pairs exist for the Bolza-type optimization problem over the solution set.
  • The value function of the optimization problem is continuous.
  • The optimal-solution map is upper semicontinuous.
  • Existence holds for min-max robust control problems under parameter uncertainty.
  • Existence holds for Hurwicz-type compromise control under parameter uncertainty.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These continuity properties may allow for numerical approximation schemes in practice.
  • The results could extend to other classes of nonsmooth dynamical systems beyond sweeping processes.
  • Parameter uncertainty handling suggests applications in uncertain environments like robotics or economics.

Load-bearing premise

The parameterized solution map possesses well-posedness, compactness, and Painlevé-Kuratowski continuity properties.

What would settle it

Finding a specific instance of the coupled system where no optimal pair exists for the Bolza problem or where the optimal-solution map fails to be upper semicontinuous despite the assumptions on the operators.

Figures

Figures reproduced from arXiv: 2607.02339 by Boris Mordukhovich, Jinsheng Du, Shengda Zeng.

Figure 1
Figure 1. Figure 1: Baseline simulation for Example 6.1: the ODE state x(t) (blue solid), sweeping state u(t) (red dash-dotted), and moving boundary β(t, u(t)) (yellow dashed). The sweeping trajectory alternates between boundary contact and interior motion while remaining feasible. In [PITH_FULL_IMAGE:figures/full_fig_p021_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Stability experiment for Example 6.1. Left: Relative error En versus ϵn ∈ [10−5 , 10−1 ] on log–log axes, together with a reference line of slope 1. Center and right: Perturbed states for ϵ ∈ {0.15, 0.08, 0.02} and the nominal trajectory ϵ = 0; the insets show deviations near active constraint intervals. III. Sensitivity of the Trajectory Cost for Example 6.1 For the same perturbation family, consider the … view at source ↗
Figure 3
Figure 3. Figure 3: shows the computed control and state response. The control remains within [−1, 1] and primarily attenuates x(t), with a smaller effect on u(t). The projected trajectory remains feasible. The objective decreases from Jnom ≈ 1.5293 to J ∗ ≈ 1.0121, a reduction of approximately 33.82%. 0 1 2 3 4 5 6 Time t -1 -0.5 0 0.5 1 C o ntrol In p ut w(t) Optimal Control Strategy Constraints '1 Optimal Control w $(t) 0 … view at source ↗
Figure 4
Figure 4. Figure 4: Joint design–control experiment for Example 6.1. Left: Optimized con￾trol. Center: Nominal and jointly optimized trajectories. Right: Feasibility relative to βη∗ (t, u∗ ). The computed values are ζ ∗ ≈ 0, η ∗ ≈ −0.15, and J ∗ ≈ 0.6945 [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Robust-control experiment for Example 6.1. Left: Cost versus ζ at η = 0.15. Center: Cost versus η at ζ = 0.25. Right: Trajectories for the computed adverse pair (0.25, 0.15). Robust optimization reduces the adverse cost from approximately 1.8726 to 1.7718. VII. Hurwicz Compromise Control for Example 6.1 Finally, for α ∈ {0, 0.1, 0.5, 0.9, 1}, we minimize Hα(w) := α inf (ζ,η)∈P J (w, ζ, η) + (1 − α) sup (ζ,… view at source ↗
Figure 6
Figure 6. Figure 6: Hurwicz-control experiment for Example 6.1. Left: Best-case, worst-case, and Hurwicz values for α ∈ {0, 0.1, 0.5, 0.9, 1}. Right: Controls at representative optimism levels; the profiles for α = 0.9 and α = 1 are nearly indistinguishable. so H(Be)(i) holds with θ(t) = 1.2t and λ = 0.3 < 1. The standard hypomonotonicity estimate for normal cones to Lipschitz translations of a ball gives ⟨v1 − v2, u1 − u2⟩ ≥… view at source ↗
Figure 7
Figure 7. Figure 7: Baseline simulation for Example 6.2. Left: ODE states x1, x2 (dashed) and sweeping states u1, u2, u3 (solid). Right: Sweeping trajectory u(t), initial ball C(0, u(0)), terminal ball C(T, u(T)), and endpoint markers. 10!4 10!3 10!2 10!1 Perturbation Magnitude 0n 10!3 10!2 10!1 R elativ e Error En Stability Analysis Numerical Error En O(0) Reference 0 1 2 3 4 5 6 Time t -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x1(… view at source ↗
Figure 8
Figure 8. Figure 8: Stability experiment for Example 6.2. Top left: Relative error En versus ϵn ∈ [10−4 , 10−1 ] on log–log axes, with a slope-one reference. Other panels: Nominal and perturbed components for ϵ ∈ {0.15, 0.08, 0.02}; the insets show intervals of rapid variation [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: shows the computed control and trajectories. The objective decreases from Jnom ≈ 9.1690 to J ∗ ≈ 8.1512, a reduction of approximately 11.10%. Most of the improvement comes from reducing ∥x(t)∥; the effect on ∥u(t)∥ is indirect through the coupling. 0 1 2 3 4 5 6 Time t -1 -0.5 0 0.5 1 C o ntrol C o m p o n e nts Optimal Vector Control w $(t) w $ 1(t) w $ 2(t) Bounds '1 0 1 2 3 4 5 6 Time t 0 0.5 1 1.5 2 2.… view at source ↗
Figure 10
Figure 10. Figure 10: Joint design–control experiment for the reduced vector benchmark. Left: Op￾timized control components. Center: Uncontrolled and optimized state norms. Right: Sweeping components and their moving lower barriers. The computed values are Jnom ≈ 3.0544, J ∗ ≈ 1.4798, ζ ∗ ≈ 0, and η ∗ = −0.15. The uncertainty set is [0, 0.5] × [−0.2, 0.2] [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: reports a direct discrete min–max computation with a blockwise-constant open-loop control. The computed inner maximizer is (ζwc, ηwc) = (0, 0.2). At this pair, the nominal-controller cost is Jnom,wc ≈ 11.1412, whereas the robust controller gives Jrob,wc ≈ 10.5764, a reduction of approximately 5.07%. The cost curves cross near ζ = 0.03–0.04, after which the robust controller performs better. In this benchm… view at source ↗
read the original abstract

We consider a class of strongly coupled nonsmooth systems consisting of a semilinear evolution inclusion and a differential inclusion governed by state-dependent maximal monotone operators. Our main contributions are fourfold. First, we collect the well-posedness, compactness, and Painlev\'e--Kuratowski continuity properties of the parameterized solution map required for the subsequent optimization analysis. Second, for Bolza-type optimization over the solution set, we prove the existence of optimal pairs, establish continuity properties of the value function, and derive upper semicontinuity of the optimal-solution map. Third, we study fixed-parameter optimal control, simultaneous control-parameter design, min--max robust control, and Hurwicz-type compromise control under parameter uncertainty, and we establish existence results for each formulation. Fourth, we report numerical experiments for sweeping-type systems that illustrate the sensitivity and robustness phenomena predicted by the theory.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript considers strongly coupled nonsmooth systems consisting of a semilinear evolution inclusion and a differential inclusion governed by state-dependent maximal monotone operators. The authors collect well-posedness, compactness, and Painlevé-Kuratowski continuity properties of the parameterized solution map. For Bolza-type optimization over the solution set they prove existence of optimal pairs, continuity properties of the value function, and upper semicontinuity of the optimal-solution map. They establish existence results for fixed-parameter optimal control, simultaneous control-parameter design, min-max robust control, and Hurwicz-type compromise control under parameter uncertainty. Numerical experiments for sweeping-type systems illustrate the predicted sensitivity and robustness phenomena.

Significance. If the well-posedness and continuity properties of the solution map hold, the work supplies a coherent framework for sensitivity analysis and robust optimal control in nonsmooth coupled systems with state-dependent maximal monotone operators. The systematic treatment of four distinct control formulations under parameter uncertainty, together with the numerical illustrations for sweeping processes, adds concrete value to the literature on set-valued optimal control.

minor comments (3)
  1. [Abstract / §2] The abstract states that the well-posedness, compactness, and Painlevé-Kuratowski continuity properties are 'collected'; a short paragraph in §2 or §3 clarifying which of these properties are proved anew versus invoked from prior literature would improve readability.
  2. [Numerical experiments] In the numerical section, the reported trajectories for the sweeping-type systems should include a brief statement of the discretization scheme and step-size used, so that the observed sensitivity phenomena can be reproduced from the given data.
  3. [Introduction] Notation for the set-valued map and the parameter dependence is introduced gradually; a consolidated table of symbols at the end of the introduction would aid readers.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the constructive and positive assessment of our manuscript, including the recognition of its contributions to well-posedness, sensitivity analysis, and the four robust control formulations. We note the recommendation for minor revision and will address any editorial or minor points in the revised version.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper first collects well-posedness, compactness, and Painlevé-Kuratowski continuity of the parameterized solution map for the coupled semilinear evolution inclusion and state-dependent maximal monotone differential inclusion, relying on standard properties of maximal monotone operators and set-valued analysis. All subsequent Bolza optimization results, value-function continuity, upper semicontinuity of the optimal-solution map, and existence theorems for the four control formulations (fixed-parameter, simultaneous design, min-max robust, Hurwicz compromise) are derived conditionally from these map properties using standard arguments from optimal control and variational analysis. No load-bearing step reduces by construction to fitted inputs, self-definitional relations, or self-citation chains that render the central claims equivalent to their premises; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no information supplied on free parameters, background axioms, or new postulated entities.

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Reference graph

Works this paper leans on

163 extracted references · 2 canonical work pages

  1. [1]

    Nonconvex sweeping process and prox-regularity in

    Bounkhel, Messaoud and Thibault, Lionel , journal=. Nonconvex sweeping process and prox-regularity in. 2005 , publisher=

    2005

  2. [2]

    2012 , publisher=

    Semigroups of Linear Operators and Applications to Partial Differential Equations , author=. 2012 , publisher=

    2012

  3. [3]

    2011 , publisher=

    Multivalued Differential Equations , author=. 2011 , publisher=

    2011

  4. [4]

    A qualitative mathematical analysis of a class of linear variational inequalities via semi-complementarity problems: applications in electronics , author=. Math. Program. , volume=. 2011 , publisher=

    2011

  5. [5]

    1982 , publisher=

    A Second Course on Real Functions , author=. 1982 , publisher=

    1982

  6. [6]

    1984 , publisher=

    Variational Convergence for Functions and Operators , author=. 1984 , publisher=

    1984

  7. [7]

    Vladimirov, A. A. , journal=. Nonstationary dissipative evolution equations in a. 1991 , publisher=

    1991

  8. [8]

    1990 , publisher=

    Set-Valued Analysis , author=. 1990 , publisher=

    1990

  9. [9]

    First and second order convex sweeping processes in reflexive smooth

    Bounkhel, Messaoud and Al-Yusof, Rabab , journal=. First and second order convex sweeping processes in reflexive smooth. 2010 , publisher=

    2010

  10. [10]

    Vietnam J

    Nonconvex sweeping process with a moving set depending on the state , author=. Vietnam J. Math. , volume=. 2014 , publisher=

    2014

  11. [11]

    Differential inclusion governed by a state dependent sweeping process , author=. Int. J. Difference Equ. , volume=

  12. [12]

    Set-Valued Var

    Sensitivity properties of parametric nonconvex evolution inclusions with application to optimal control problems , author=. Set-Valued Var. Anal. , volume=. 2019 , publisher=

    2019

  13. [13]

    Mixed semicontinuous perturbations of nonconvex sweeping processes , author=. Math. Program. , volume=. 2010 , publisher=

    2010

  14. [14]

    Regularization of differential variational inequalities with locally prox-regular sets , author=. Math. Program. , volume=. 2013 , publisher=

    2013

  15. [15]

    Set-Valued Anal

    Non-convex quasi-variational differential inclusions , author=. Set-Valued Anal. , volume=. 2007 , publisher=

    2007

  16. [16]

    2006 , publisher=

    Edmond, Jean Fenel and Thibault, Lionel , journal=. 2006 , publisher=

    2006

  17. [17]

    Convex Analysis and Measurable Multifunctions , pages=

    Measurable multifunctions , author=. Convex Analysis and Measurable Multifunctions , pages=. 2006 , publisher=

    2006

  18. [18]

    and Obukhovskii, Valeri V

    Kamenskii, Mikhail I. and Obukhovskii, Valeri V. and Zecca, Pietro , volume=. Condensing Multivalued Maps and Semilinear Differential Inclusions in. 2011 , publisher=

    2011

  19. [19]

    Existence and Uniqueness of Infinite Dimensional Dynamic Systems Governed by History/State-Dependent Sweeping Processes , author=

  20. [20]

    Zeng, Shengda and Du, Jinsheng and Timoshin, Sergey A. , note=. Non-Autonomous Evolution Inclusions with State-Dependent Sweeping Processes:

  21. [21]

    Well-Posedness and Painlev

    Zeng, Shengda and Du, Jinsheng and Wang, Xianfu , note=. Well-Posedness and Painlev

  22. [22]

    2017 , publisher=

    Variational-Hemivariational Inequalities with Applications , author=. 2017 , publisher=

    2017

  23. [23]

    1992 , publisher=

    Measures of Noncompactness and Condensing Operators , author=. 1992 , publisher=

    1992

  24. [24]

    1990 , publisher=

    Optimization and Nonsmooth Analysis , author=. 1990 , publisher=

    1990

  25. [25]

    Dynamical systems coupled with monotone set-valued operators:

    Brogliato, Bernard and Tanwani, Aneel , journal=. Dynamical systems coupled with monotone set-valued operators:. 2020 , publisher=

    2020

  26. [26]

    1998 , publisher=

    Nonsmooth Analysis and Control Theory , author=. 1998 , publisher=

    1998

  27. [27]

    Nonlinear Anal

    On various notions of regularity of sets in nonsmooth analysis , author=. Nonlinear Anal. , volume=. 2002 , publisher=

    2002

  28. [28]

    Nonconvex differential variational inequality and state-dependent sweeping process , author=. J. Optim. Theory Appl. , volume=. 2013 , publisher=

    2013

  29. [29]

    Truncated nonconvex state-dependent sweeping process: implicit and semi-implicit adapted

    Nacry, Florent , journal=. Truncated nonconvex state-dependent sweeping process: implicit and semi-implicit adapted. 2018 , publisher=

    2018

  30. [30]

    Rafle par un convexe variable (premi

    Moreau, Jean Jacques , journal=. Rafle par un convexe variable (premi

  31. [31]

    Rafle par un convexe variable (deuxi

    Moreau, Jean Jacques , journal=. Rafle par un convexe variable (deuxi

  32. [32]

    A method using the approach of

    Addi, Khalid and Adly, Samir and Brogliato, Bernard and Goeleven, Daniel , journal=. A method using the approach of. 2007 , publisher=

    2007

  33. [33]

    Kunze, Markus and Monteiro Marques, Manuel D. P. , booktitle=. An introduction to. 2000 , publisher=

    2000

  34. [34]

    2018 , publisher=

    A Variational Approach to Nonsmooth Dynamics: Applications in Unilateral Mechanics and Electronics , author=. 2018 , publisher=

    2018

  35. [35]

    On parabolic quasi-variational inequalities and state-dependent sweeping processes , author=. Topol. Methods Nonlinear Anal. , volume=

  36. [36]

    2010 , publisher=

    Nonsmooth Modeling and Simulation for Switched Circuits , author=. 2010 , publisher=

    2010

  37. [37]

    A differential equation approach to implicit sweeping processes , author=. J. Differential Equations , volume=. 2019 , publisher=

    2019

  38. [38]

    Implicit subdifferential inclusions with nonconvex-valued perturbations , author=. J. Fixed Point Theory Appl. , volume=. 2021 , publisher=

    2021

  39. [39]

    State-dependent implicit sweeping process in the framework of quasistatic evolution quasi-variational inequalities , author=. J. Optim. Theory Appl. , volume=. 2019 , publisher=

    2019

  40. [40]

    Well-posedness of fractional

    Zeng, Shengda and Haddad, Tahar and Bouach, Abderrahim , journal=. Well-posedness of fractional. 2023 , publisher=

    2023

  41. [41]

    A coupled problem described by time-dependent subdifferential operator and non-convex perturbed sweeping process , author=. Evol. Equ. Control Theory , volume=

  42. [42]

    arXiv preprint arXiv:2407.16304 , year=

    Lipschitz multivalued perturbations of integro-differential prox-regular sweeping processes , author=. arXiv preprint arXiv:2407.16304 , year=

    work page arXiv

  43. [43]

    Galerkin-like method and generalized perturbed sweeping process with nonregular sets , author=. SIAM J. Control Optim. , volume=. 2017 , publisher=

    2017

  44. [44]

    Fractional-order problem coupled with a second-order

    Tamouza, Somia and Aliouane, Fatine and Azzam-Laouir, Dalila , journal=. Fractional-order problem coupled with a second-order. 2023 , publisher=

    2023

  45. [45]

    Set-Valued Var

    On a time and state dependent maximal monotone operator coupled with a sweeping process with perturbations , author=. Set-Valued Var. Anal. , volume=. 2021 , publisher=

    2021

  46. [46]

    A maximum principle for optimal control problems involving sweeping processes with a nonsmooth set , author=. J. Optim. Theory Appl. , volume=. 2023 , publisher=

    2023

  47. [47]

    Semialgebraic Geometric Methods , author=

    An Approach to Simultaneous System Design, I. Semialgebraic Geometric Methods , author=. SIAM J. Control Optim. , volume=. 1986 , doi=

    1986

  48. [48]

    Part II: Nonswitching Gain and Dynamic Feedback Compensation by Algebraic Geometric Methods , author=

    An Approach to Simultaneous System Design. Part II: Nonswitching Gain and Dynamic Feedback Compensation by Algebraic Geometric Methods , author=. SIAM J. Control Optim. , volume=. 1988 , doi=

    1988

  49. [49]

    Relaxed Minimax Control , author=. SIAM J. Control Optim. , volume=. 1995 , doi=

    1995

  50. [50]

    Minimax Optimal Control , author=. SIAM J. Control Optim. , volume=. 2005 , doi=

    2005

  51. [51]

    Stability and Continuity in Robust Optimization , author=. SIAM J. Optim. , volume=. 2017 , doi=

    2017

  52. [52]

    Studies in Resource Allocation Processes , pages=

    Appendix: An Optimality Criterion for Decision-Making Under Ignorance , author=. Studies in Resource Allocation Processes , pages=. 1977 , publisher=

    1977

  53. [53]

    2009 , publisher=

    Robust Optimization , author=. 2009 , publisher=

    2009

  54. [54]

    2008 , publisher=

    Ba. 2008 , publisher=

    2008

  55. [55]

    Systems Control Lett

    Minimax sliding mode control design for linear evolution equations with noisy measurements and uncertain inputs , author=. Systems Control Lett. , volume=. 2021 , doi=

    2021

  56. [56]

    Sensitivity of Optimal Solutions to Control Problems for Second Order Evolution Subdifferential Inclusions , author=. Appl. Math. Optim. , volume=. 2015 , doi=

    2015

  57. [57]

    Differentiating ambiguity and ambiguity attitude , author=. J. Econom. Theory , volume=. 2004 , doi=

    2004

  58. [58]

    2002 , publisher=

    Foundations of Bilevel Programming , author=. 2002 , publisher=

    2002

  59. [59]

    Discrete Contin

    Optimality conditions for a controlled sweeping process with applications to the crowd motion model , author=. Discrete Contin. Dyn. Syst. Ser. B , volume=. 2017 , doi=

    2017

  60. [60]

    Maxmin expected utility with non-unique prior , author=. J. Math. Econom. , volume=. 1989 , doi=

    1989

  61. [61]

    1996 , publisher=

    Robust and Optimal Control , author=. 1996 , publisher=

    1996

  62. [62]

    2000 , publisher=

    Perturbation Analysis of Optimization Problems , author=. 2000 , publisher=

    2000

  63. [63]

    Optimal control of sweeping processes in robotics and traffic flow models , author=. J. Optim. Theory Appl. , volume=. 2019 , publisher=

    2019

  64. [64]

    Optimal control of nonconvex integro-differential sweeping processes , author=. J. Differential Equations , volume=. 2022 , publisher=

    2022

  65. [65]

    Optimal control of a nonconvex perturbed sweeping process , author=. J. Differential Equations , volume=. 2019 , publisher=

    2019

  66. [66]

    Controlled polyhedral sweeping processes:

    Henrion, Ren. Controlled polyhedral sweeping processes:. J. Differential Equations , volume=. 2023 , publisher=

    2023

  67. [67]

    Sweeping process with regular and nonregular sets , author=. J. Differential Equations , volume=. 2003 , publisher=

    2003

  68. [68]

    Relaxation of an optimal control problem involving a perturbed sweeping process , author=. Math. Program. , volume=. 2005 , publisher=

    2005

  69. [69]

    Optimal control of the sweeping process with a nonsmooth moving set , author=. SIAM J. Control Optim. , volume=. 2022 , publisher=

    2022

  70. [70]

    A fixed-point approach to history-dependent sweeping processes , author=. J. Optim. Theory Appl. , volume=. 2025 , publisher=

    2025

  71. [71]

    Well-posedness of history-dependent sweeping processes , author=. SIAM J. Math. Anal. , volume=. 2019 , publisher=

    2019

  72. [72]

    Galerkin-like Method for Integro-Differential Inclusions with applications to

    P. Galerkin-like Method for Integro-Differential Inclusions with applications to. arXiv preprint arXiv:2306.07821 , year=

    work page arXiv

  73. [73]

    Well-posedness for integro-differential sweeping processes of

    Vilches, Emilio , journal=. Well-posedness for integro-differential sweeping processes of

  74. [74]

    Prox-Regular Integro-Differential Sweeping Process , author=. J. Optim. Theory Appl. , volume=. 2024 , publisher=

    2024

  75. [75]

    Nonconvex integro-differential sweeping process with applications , author=. SIAM J. Control Optim. , volume=. 2022 , publisher=

    2022

  76. [76]

    Well-posedness of a class of

    Faiz, Zakaria and Zeng, Shengda and Benaissa, Hicham , journal=. Well-posedness of a class of. 2025 , publisher=

    2025

  77. [77]

    A novel fractional

    Faiz, Zakaria and Zeng, Shengda and Benaissa, Hicham , journal=. A novel fractional. 2024 , publisher=

    2024

  78. [78]

    Well-posedness of history/state-dependent implicit sweeping processes , author=. J. Optim. Theory Appl. , volume=. 2020 , publisher=

    2020

  79. [79]

    An implicit sweeping process approach to quasistatic evolution variational inequalities , author=. SIAM J. Math. Anal. , volume=. 2018 , publisher=

    2018

  80. [80]

    Regularization of nonconvex sweeping process in

    Thibault, Lionel , journal=. Regularization of nonconvex sweeping process in. 2008 , publisher=

    2008

Showing first 80 references.