We address an optimization problem in which two agents, each with a set of weighted items, compete in order to minimize the total weight of their solution sets. The latter are built according to a sequential game consisting in a fixed number of rounds. In every round each agent submits one item that may be … Read more
The bundle-level method and their certain variants are known to exhibit an optimal rate of convergence, i.e., ${\cal O}(1/\sqrt{t})$, and also excellent practical performance for solving general non-smooth convex programming (CP) problems. However, this rate of convergence is significantly worse than the optimal one for solving smooth CP problems, i.e., ${\cal O}(1/t^2)$. In this paper, … Read more
In this paper, we consider a class of inexact proximal point methods for convex optimization which allows a relative error tolerance in the approximate solution of each proximal subproblem. By exploiting the special structure of convex optimization problems, we are able to derive surprising complexity bounds for the aforementioned class. As a consequence, we show … Read more
In this paper, we consider the monotone inclusion problem consisting of the sum of a continuous monotone map and a point-to-set maximal monotone operator with a separable two-block structure and introduce a framework of block-decomposition prox-type algorithms for solving it which allows for each one of the single-block proximal subproblems to be solved in an … Read more
In this paper, we propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In our problem, besides the convex point-wise constraints on state variables, we have convex coupling constraints with finite-dimensional image. Hence, we can formulate a finite-dimensional dual problem, which can be solved by efficient gradient methods. … Read more
In this paper, we consider both a variant of Tseng’s modified forward-backward splitting method and an extension of Korpelevich’s method for solving generalized variational inequalities with Lipschitz continuous operators. By showing that these methods are special cases of the hybrid proximal extragradient (HPE) method introduced by Solodov and Svaiter, we derive iteration-complexity bounds for them … Read more
In this paper we present a generic algorithmic framework, namely, the accelerated stochastic approximation (AC-SA) algorithm, for solving strongly convex stochastic composite optimization (SCO) problems. While the classical stochastic approximation (SA) algorithms are asymptotically optimal for solving differentiable and strongly convex problems, the AC-SA algorithm, when employed with proper stepsize policies, can achieve optimal or … Read more
This paper focuses on the aircraft landing problem that is to assign landing times to aircraft approaching the airport under consideration. Each aircraft’s landing time must be in a time interval encompassing a target landing time. If the actual landing time deviates from the target landing time additional costs occur which depend on the amount … Read more
In this paper, we study polynomial-time interior-point algorithms in view of information geometry. We introduce an information geometric structure for a conic linear program based on a self-concordant barrier function. Riemannian metric is defined with the Hessian of the barrier function. We introduce two connections $\nabla$ and $\nabla^*$ which roughly corresponds to the primal and … Read more
In this paper we deal with the Critical Node Problem (CNP), i.e., the problem of searching for a given number K of nodes in a graph G, whose removal minimizes the number of connections between pairs of nodes in the residual graph. While the NP-completeness of this problem for general graphs has been already established … Read more