Related papers: On constrained optimization problems solved using …
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
Learning to Optimize (LtO) is a problem setting in which a machine learning (ML) model is trained to emulate a constrained optimization solver. Learning to produce optimal and feasible solutions subject to complex constraints is a difficult…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
The formalism of Causal Dynamical Triangulations (CDT) attempts to provide a non-perturbative regularization of quantum gravity, viewed as an ordinary quantum field theory. In two dimensions one can solve the lattice theory analytically and…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where…
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…
This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform…
Canonical Correlation Analysis (CCA) is widely used for multimodal data analysis and, more recently, for discriminative tasks such as multi-view learning; however, it makes no use of class labels. Recent CCA methods have started to address…
We model the cardinality-constrained portfolio problem using semidefinite matrices and investigate a relaxation using semidefinite programming. Experimental results show that this relaxation generates tight lower bounds and even achieves…
In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
We discuss the algorithmic problem of minimal coupling gauge fields of the Yang-Mills type to Quantum Gravity in the approach known as Causal Dynamical Triangulations (CDT) as a step towards studying, ultimately, systems of gravity coupled…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
Self-Supervised Learning (SSL) for Combinatorial Optimization (CO) is an emerging paradigm for solving combinatorial problems using neural networks. In this paper, we address a central challenge of SSL for CO: solving problems with discrete…
The Distributed Constraint Optimization Problem (DCOP) formulation is a powerful tool to model multi-agent coordination problems that are distributed by nature. The formulation is suitable for problems where variables are discrete and…