Related papers: A Minimaxmax Problem for Improving the Torsional S…

We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For…

Vibrational structures are susceptible to catastrophic failures or structural damages when external forces induce resonances or repeated unwanted oscillations. One common mitigation strategy is to use dampers to suppress these disturbances.…

This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization…

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator.…

The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This…

We give a short and easy upper bound on the worst-case size of fault tolerant spanners, which improves on all prior work and is fully optimal at least in the setting of vertex faults.

In this article we consider min-min type of problems or minimization by two groups of variables. Min-min problems may occur in case if some groups of variables in convex optimization have different dimensions or if these groups have…

Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…

We present and analyze a new finite element method for solving interface problems on a triangular grid. The method locally modifies a given triangulation such that the interfaces are accurately resolved and the maximal angle condition…

We introduce a new class of inverse optimization problems in which an input solution is given together with $k$ linear weight functions, and the goal is to modify the weights by the same deviation vector $p$ so that the input solution…

Given two hyperbolic surfaces and a homotopy class of maps between them, Thurston proved that there always exists a representative minimizing the Lipschitz constant. While not unique, these minimizers are rigid along a geodesic lamination.…

We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…

We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…

Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimization are often based on techniques from differential…

We introduce and study Minimum Cut Representability, a framework to solve optimization and feasibility problems over stable matchings by representing them as minimum s-t cut problems on digraphs over rotations. We provide necessary and…

The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

In this work, we investigate a novel approach for the simulation of two-dimensional, brittle, quasi-static fracture problems based on a shape optimization approach. In contrast to the commonly-used phase-field approach, this proposed…

This paper presents a method for simultaneous optimization of the outer shape and internal topology of aircraft wings, with the objective of minimizing drag subject to lift and compliance constraints for multiple load cases. The physics are…

Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solvability of these problems in both the unconstrained and the…