Related papers: A Minimaxmax Problem for Improving the Torsional S…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
This paper introduces a novel design method that enhances the force/torque, bendability, and controllability of soft pneumatic actuators (SPAs). The complex structure of the soft actuator is simplified by approximating it as a cantilever…
In this paper, we focus on the nonconvex-strongly-concave minimax optimization problem (MCC), where the inner maximization subproblem contains constraints that couple the primal variable of the outer minimization problem. We prove that by…
We consider the problem of placing n small balls of given radius in a certain domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look at the asymptotics of the…
Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as well as from tradition research areas such as saddle point…
We investigate the torsion function or landscape function and its integral, the torsional rigidity, of Laplacians on metric graphs subject to $\delta$-vertex conditions. A variational characterization of torsional rigidity and Hadamard-type…
We study minimax lower bounds for function estimation problems on large graph when the target function is smoothly varying over the graph. We derive minimax rates in the context of regression and classification problems on graphs that…
In this paper we consider a minimization problem of the type $$ I_{\beta,p}(D;\Omega)=\inf\biggl\{\int_\Omega \lvert{D\phi}\rvert^pdx+\beta \int_{\partial^* \Omega}\lvert{\phi}\rvert^pd\mathcal{H}^{n-1},\; \phi \in W^{1,p}(\Omega),\;\phi…
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
In this paper, stress-constrained topology optimization is applied to the design of compliant displacement magnification mechanisms. By formulating the objective function based on the concept of effective energy, it is not necessary to…
In this work, we consider constrained stochastic optimization problems under hidden convexity, i.e., those that admit a convex reformulation via non-linear (but invertible) map $c(\cdot)$. A number of non-convex problems ranging from…
A multiobjective optimization method is proposed for obtaining the optimal plane trusses simultaneously for various aspect ratios of the initial ground structure as a set of Pareto optimal solutions generated through a single optimization…
We address an optimal reachability problem for a planar manipulator in a constrained environment. After introducing the optmization problem in full generality, we practically embed the geometry of the workspace in the problem, by…
The present paper treats the problem of finding the asymptotic bounds for the globally optimal locations of orthogonal stiffeners minimizing the compliance of a rectangular plate in elastostatic bending. The essence of the paper is the…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
An adjoint-based optimization is applied to study the thrust performance of a pitching-rolling ellipsoidal plate in a uniform stream at Reynolds number 100. To achieve the highest thrust, the optimal kinematics of pitching-rolling motion is…
In this paper, we address the problem of interpolation of smooth convex-concave functions. Interpolation is a key step for computer-assisted estimation of worst-case performance via PEP-like techniques, and smooth convex-concave functions…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…