The work by Gould, Loh, and Robinson [A filter method with unified step computation for nonlinear optimization, SIAM J. Optim., 24 (2014), pp. 175–209 ] established global convergence of a new filter line search method for finding local first-order solutions to nonlinear and nonconvex constrained optimization problems. A key contribution of that work was that the search direction was computed u...

Aggregates in answer set programming (ASP) have recently been studied quite intensively. The main focus of previous work has been on defining suitable semantics for programs with arbitrary, potentially recursive aggregates. By now, these efforts appear to be converging. An interesting feature of the respective semantics is that for programs without disjunctive rules, the complexity of reasoning...

This work is a continuation of our previous papers devoted to exploration of the regular search procedures efficiency in binary search spaces. Here we formulate the problem in a rather general form as a problem of optimization of an unimodal pseudoboolean function given implicitly and obtain analitical estimates of the expected time of a minimum point search for procedures of direct local searc...

In this paper, based on the regularization techniques and projected gradient strategies, we present a quadratic regularization projected alternating Barzilai–Borwein (QRPABB) method for minimizing differentiable functions on closed convex sets. We show the convergence of the QRPABB method to a constrained stationary point for a nonmonotone line search. When the objective function is convex, we ...

The paper presents a semismooth inexact Newton-type method for solving optimal power flow (OPF) problem. By introducing the nonlinear complementarity problem (NCP) function, the Karush-KuhnTucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by an improved inexact LevenbergMar...

An efficient gradient-based method to solve the volume constrained topology optimization problems is presented. Each iterate of this algorithm is obtained by the projection of a Barzilai-Borwein step onto the feasible set consisting of box and one linear constraints (volume constraint). To ensure the global convergence, an adaptive nonmonotone line search is performed along the direction that i...

In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [1] with a modification of the nonmonotone line search framework recently proposed in [2]. In the first stage, the algorithm exploits a property of the active-set estimate that ensures a significant reduction of the objective function when sett...

Abstract. We analyze an abridged version of the active-set algorithm FPC AS proposed in [18] for solving the l1-regularized problem, i.e., a weighted sum of the l1-norm ‖x‖1 and a smooth function f(x). The active set algorithm alternatively iterates between two stages. In the first “nonmonotone line search (NMLS)” stage, an iterative first-order method based on “shrinkage” is used to estimate t...

In this work we propose a variant of the inexact Newton method for the solution of semismooth nonlinear systems of equations. We introduce a nonmonotone scheme, which couples the inexact features with the nonmonotone strategies. For the nonmonotone scheme, we present the convergence theorems. Finally, we show how we can apply these strategies in the variational inequalities context and we prese...

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with Hölder continuous gradients. The proposed schemes are optimal for smooth strongly convex problems with Lipschitz continuous gradients and optimal up to a logarithmic fac...