相关论文: On unconstrained optimization problems solved usin…

We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed…

We provide a spectrum of new theoretical insights and practical results for finding a Minimum Dilation Triangulation (MDT), a natural geometric optimization problem of considerable previous attention: Given a set $P$ of $n$ points in the…

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…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

Optimal transport (OT) theory describes general principles to define and select, among many possible choices, the most efficient way to map a probability measure onto another. That theory has been mostly used to estimate, given a pair of…

Classical primal-dual affine programming takes place over finite dimensional real vector spaces. This results in beautiful duality theory, connecting the optimal solu- tions of the primal maximization problem and the dual minimization…

In sphere of research of discrete optimization algorithms efficiency the important place occupies a method of polynomial reducibility of some problems to others with use of special purpose components. In this paper a novel method of compact…

This is a survey on selected developments in the theory of natural dualities where the author had the opportunity to make with his foreign colleagues several breakthroughs and move the theory forward. It is aimed as author's reflection on…

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…

Using variational methods, we obtain several multiplicity results for double phase problems that involve variable exponents and a new type of critical growth. This new critical growth is better suited for double phase problems when compared…

Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…

Optimization Modulo Theories (OMT) has emerged as an important extension of the highly successful Satisfiability Modulo Theories (SMT) paradigm. The OMT problem requires solving an SMT problem with the restriction that the solution must be…

Delays and asynchrony are inevitable in large-scale machine-learning problems where communication plays a key role. As such, several works have extensively analyzed stochastic optimization with delayed gradients. However, as far as we are…

Gauge functions significantly generalize the notion of a norm, and gauge optimization, as defined by Freund (1987}, seeks the element of a convex set that is minimal with respect to a gauge function. This conceptually simple problem can be…

A new technique of global optimization and its applications in particular to neural networks are presented. The algorithm is also compared to other global optimization algorithms such as Gradient descent (GD), Monte Carlo (MC), Genetic…

We consider a model of restricted dimers coupled to two-dimensional causal dynamical triangulations (CDT), where the dimer configurations are restricted in the sense that they do not include dimers in regions of high curvature. It is shown…

This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite…

We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…

Optimal transport (OT) theory underlies many emerging machine learning (ML) methods nowadays solving a wide range of tasks such as generative modeling, transfer learning and information retrieval. These latter works, however, usually build…

This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…