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One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…
Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem is non-convex when considering standard Barrier and Density methods for invariant sets, and has been treated heuristically by…
We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…
We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…
Given an undirected graph and a size parameter $k$, the Densest $k$-Subgraph (D$k$S) problem extracts the subgraph on $k$ vertices with the largest number of induced edges. While D$k$S is NP--hard and difficult to approximate, penalty-based…
We propose a computational approach to constructing exact designs on finite design spaces that are optimal for multiresponse regression experiments under a combination of the standard linear and specific 'sparsity' constraints. The linear…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
The maximum traveling salesman problem (Max TSP) consists of finding a Hamiltonian cycle with the maximum total weight of the edges in a given complete weighted graph. This problem is APX-hard in the general metric case but admits…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
The superelastic constitutive model implemented in the commercial finite element code ABAQUS is verified using the method of exact solutions (MES). An analytical solution for uniaxial strain is first developed under a set of simplifying…
A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions for a class of statistical decision problems. In particular, we are interested in…
We efficiently solve the optimal multi-dimensional mechanism design problem for independent bidders with arbitrary demand constraints when either the number of bidders is a constant or the number of items is a constant. In the first…
We develop the max-plus finite element method to solve finite horizon deterministic optimal control problems. This method, that we introduced in a previous work, relies on a max-plus variational formulation, and exploits the properties of…
Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…
This paper addresses a class of problems under interval data uncertainty composed of min-max regret versions of classical 0-1 optimization problems with interval costs. We refer to them as interval 0-1 min-max regret problems. The…
We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…