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This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness…

We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match with that of physical degrees of freedom…

Integrated learning and optimization (ILO) is a framework in contextual optimization which aims to train a predictive model for the probability distribution of the underlying problem data uncertainty, with the goal of enhancing the quality…

Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…

Modern world models are becoming too complex to admit explicit dynamical descriptions. We study safety-critical contextual control, where a Planner must optimize a task objective using only feasibility samples from a black-box Simulator,…

We study a pointwise tracking optimal control problem for the stationary Navier--Stokes equations; control constraints are also considered. The problem entails the minimization of a cost functional involving point evaluations of the state…

Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…

In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…

The aim of this paper is to give a simpler, more usable sufficient condition to the regularity of generic weakly stationary time series. Also, this condition is used to show how regular processes satisfying these sufficient conditions can…

We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…

The goal of this paper is to address finite-horizon minimum variance and covariance steering problems for discrete-time stochastic (Gaussian) linear systems. On the one hand, the minimum variance problem seeks for a control policy that will…

We consider stochastic approximations which arise from such applications as data communications and image processing. We demonstrate why constraints are needed in a stochastic approximation and how a constrained approximation can be…

This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…

In this paper, we investigate second-order necessary conditions and exact penalty of mathematical programs with switching constraints (MPSC). Some new second-order constraint qualifications and second-order quasi-normality are introduced…

Mathematical programs with disjunctive constraints (MPDCs for short) cover several different problem classes from nonlinear optimization including complementarity-, vanishing-, cardinality-, and switching-constrained optimization problems.…

For an arbitrary finite family of semi-algebraic/definable functions, we consider the corresponding inequality constraint set and we study qualification conditions for perturbations of this set. In particular we prove that all positive…

Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration…

In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent…

Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…