We consider the optimal control of a PDE with random source term subject to probabilistic or almost sure state constraints. In the main theoretical result, we provide an exact formula for the Clarke subdifferential of the probability function ...

We propose two iterative algorithms for solving two classes of quasi-equilibrium problems in Hilbert spaces: pseudomonotone and quasimonotone ones. The algorithms combine the subgradient method and the projection method with self-adaptive step ...

We explore and construct an enlarged subdifferential for weakly convex functions. The resulting object turns out to be continuous with respect to both the function argument and the enlargement parameter. We carefully analyze connections with other ...

In this paper, we characterize Lipschitzian properties of different multiplier-free and multiplier-dependent perturbation mappings associated with the stationarity system of a so-called generalized nonlinear program popularized by Rockafellar. ...

Variational inequality (VI) generalizes many mathematical programming problems and has a wide variety of applications. One class of VI solution methods is to reformulate a VI into a normal map nonsmooth equation system, which is then solved using ...

We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger ...

The efficient optimization method for locally Lipschitz continuous multiobjective optimization problems from Gebken and Peitz (J Optim Theory Appl 188:696–723, 2021) is extended from finite-dimensional problems to general Hilbert spaces. The ...

Two new accelerated fixed-time stable dynamic systems are proposed for solving absolute value equations (AVEs): $Ax-|x|-b=0$. Under some mild conditions, the equilibrium point of the proposed dynamic systems is completely equivalent to the solution ...

In this paper, we propose a new splitting algorithm to find the zero of a monotone inclusion problem that features the sum of three maximal monotone operators and a Lipschitz continuous monotone operator in Hilbert spaces. We prove that the ...

In this paper, we use the distributionally robust approach to study stochastic variational inequalities under the ambiguity of the true probability distribution, which is referred to as distributionally robust variational inequalities (DRVIs). ...

In this paper, we study a class of variational inequality problems the constraint set of which is the set of common solutions of a finite family of operator equations, involving hemi-continuous accretive operators on a reflexive and strictly ...

This work introduces a new Riemannian optimization method for registering open parameterized surfaces with a constrained global optimization approach. The proposed formulation leads to a rigorous theoretic foundation and guarantees the existence ...

The notion of sharp minima, given by Polyak, is an important tool in studying the convergence analysis of algorithms designed to solve optimization problems. It has been studied extensively for variational inequality problems and equilibrium ...

For constrained equations with nonisolated solutions and a certain family of Newton-type methods, it was previously shown that if the equation mapping is 2-regular at a given solution with respect to a direction which is interior feasible and ...

Having in mind singular solutions of smooth reformulations of complementarity problems, arising unavoidably when the solution in question violates strict complementarity, we study the behavior of Newton-type methods near singular solutions of ...

We give a rigorous complexity analysis of the simulated annealing algorithm by Kalai and Vempala (Math Oper Res 31(2):253–266, 2006) using the type of temperature update suggested by Abernethy and Hazan (International Conference on Machine ...

In this paper, we provide a necessary and sufficient condition under which the method of alternating projections on Hadamard spaces converges strongly. This result is new even in the context of Hilbert spaces. In particular, we found the ...

This paper aims to establish higher order convergence of the (inexact) Newton’s method for solving generalized equations composed of the sum of a single-valued mapping and a set-valued mapping between arbitrary Banach spaces without Lipschitz ...

The nonlinear filtering problem plays a fundamental role in multiple space-related applications. This paper offers a new filtering technique that combines Monte Carlo time propagation with a Gaussian mixture model measurement update. Differential ...

We are concerned with the tensor equations whose coefficient tensors are M-tensors. We first propose a Newton method for solving the equation with a positive constant term and establish its global and quadratic convergence. Then we extend the ...