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Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
Leveraging machine learning methods to solve constraint satisfaction problems has shown promising, but they are mostly limited to a static situation where the problem description is completely known and fixed from the beginning. In this…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…
For the first time, a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions is analyzed. The investigated problem involves a nonlinear monotone partial differential equation in the interior…
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…
Constrained reinforcement learning is to maximize the expected reward subject to constraints on utilities/costs. However, the training environment may not be the same as the test one, due to, e.g., modeling error, adversarial attack,…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box.…
We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem $-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$ on a bounded domain $\Omega \subset \R^N$, which…
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…
Newton's method has been an important approach for solving variational inequalities, quasi-Newton method is a good alternative choice to save computational cost. In this paper, we propose a new method for solving monotone variational…
The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only…
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…
The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
We investigate a fixed domain approach in shape optimization, using a regularization of the Heaviside function both in the cost functional and in the state system. We consider the compliance minimization problem in linear elasticity, a well…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
Constrained submodular maximization has been extensively studied in the recent years. In this paper, we study adaptive robust optimization with nearly submodular structure (ARONSS). Our objective is to randomly select a subset of items that…