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In the study of stochastic mixed variational inequalities(SMVIs), Lipschitz is an indispensable assumption for the convergence analysis. However, practical applications may not satisfy this assumption. In this paper, we propose a stochastic ...

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 ...

This paper proposes two innovative vector transport operators, leveraging the Cayley transform, for the generalized Stiefel manifold embedded with a non-standard metric. Specifically, it introduces the differentiated retraction and an ...

In this paper, we study the standard formulation of an optimization problem when the computation of gradient is not available. Such a problem can be classified as a “black box” optimization problem, since the oracle returns only the value of the ...

We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $l\le d$ orthogonal directions, where d is the dimension of the ambient space. These ...${}^{}$$\mathrm{}\mathrm{}$

Stochastic first-order methods are standard for training large-scale machine learning models. Random behavior may cause a particular run of an algorithm to result in a highly suboptimal objective value, whereas theoretical guarantees are usually ...

The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth equations. In ...$$

Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions, and a central limit ...

This paper investigates a type of minimax linear fractional program (MLFP) that often occurs in practical problems such as design of electronic circuits, finance and investment. We first transform the MLFP problem into an equivalent problem (EP) ...

This paper presents a subgradient-based algorithm for constrained nonsmooth convex optimization that does not require projections onto the feasible set. While the well-established Frank–Wolfe algorithm and its variants already avoid projections, ...$$$\mathcal{}{}^{\mathrm{}}$

This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a robust ...

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). ...

This contribution presents substantial computational advancements to compare measures even with varying masses. Specifically, we utilize the nonequispaced fast Fourier transform to accelerate the radial kernel convolution in unbalanced optimal ...$\mathcal{}\left({}^{\mathrm{}}\right)$$\mathcal{}\left(,,\right)$

In this paper, we deal with risk evaluation and risk-averse optimization of complex distributed systems with general risk functionals. We postulate a novel set of axioms for the functionals evaluating the total risk of the system. We derive a dual ...

Nonlinear dependence on a probability measure has recently been encountered with increasing intensity in stochastic optimization. This type of dependence corresponds to many situations in applications; it can appear in problems static (one-stage), ...${\mathcal{}}_{\mathrm{}}$

In this paper we investigate optimal control problems perturbed by random events. We assume that the control has to be decided prior to observing the outcome of the perturbed state equations. We investigate the use of probability functions in the ...

Several classical adaptive optimization algorithms, such as line search and trust-region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic ...

Scenario optimization is an approach to data-driven decision-making that has been introduced some fifteen years ago and has ever since then grown fast. Its most remarkable feature is that it blends the heuristic nature of data-driven methods with ...

This paper deals with operational fixed interval scheduling problems under uncertainty caused by random delays. This stochastic programming problem has a deterministic reformulation based on network flow under the assumption that the machines are ...

• Fixed interval scheduling problems under uncertainty are considered.
• Heterogeneous machines and job classes are incorporated.
• A Lagrangian relaxation algorithm is proposed.
• Efficient lower and upper bounding procedures are ...

The existing stochastic approximation (SA)-type algorithms for two-stage stochastic variational inequalities (SVIs) are based on the uniqueness of the second-stage solution, which restricts the use of those algorithms. In this paper, we propose a ...$\mathit{}\mathbf{}\mathbf{}\sqrt{\mathit{}}$