Related papers: BiqBin: a parallel branch-and-bound solver for bin…
Maintaining the pair similarity relationship among originally high-dimensional data into a low-dimensional binary space is a popular strategy to learn binary codes. One simiple and intutive method is to utilize two identical code matrices…
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…
High Performance Computing is notorious for its long and expensive software development cycle. To address this challenge, we present Bind: a "partitioned global workflow" parallel programming model for C++ applications that enables quick…
We present algorithm MIQCR-CB that is an advancement of method MIQCR~(Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving mixed-integer quadratic programs and works in two phases: the first phase determines an equivalent…
The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP.…
In this paper, we present a new method to solve a certain type of Semidefinite Programming (SDP) problems. These types of SDPs naturally arise in the Quadratic Convex Reformulation (QCR) method and can be used to obtain dual bounds of…
Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with…
Inverse source problems arise often in real-world applications, such as localizing unknown groundwater contaminant sources. Being different from Tikhonov regularization, the quasi-boundary value method has been proposed and analyzed as an…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…
When solving numerical constraints such as nonlinear equations and inequalities, solvers often exploit pruning techniques, which remove redundant value combinations from the domains of variables, at pruning steps. To find the complete…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
Decision trees are one of the most useful and popular methods in the machine learning toolbox. In this paper, we consider the problem of learning optimal decision trees, a combinatorial optimization problem that is challenging to solve at…
In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node…
Quadratic unconstrained binary optimization (QUBO) provides problem formulations for various computational problems that can be solved with dedicated QUBO solvers, which can be based on classical or quantum computation. A common approach to…