Direct-search methods are a class of popular derivative-free algorithms characterized by evaluating the objective function using a step size and a number of (polling) directions. When applied to the minimization of smooth functions, the polling directions are typically taken from positive spanning sets which in turn must have at least n+1 vectors in an n-dimensional variable space. In addition,...

Direct search is a methodology for derivative-free optimization whose iterations are characterized by evaluating the objective function using a set of polling directions. In deterministic direct search applied to smooth objectives, these directions must somehow conform to the geometry of the feasible region and typically consist of positive generators of approximate tangent cones (which then re...

A novel primal-dual path-following interior-point algorithm for the Cartesian P∗(κ)-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-u...

We propose an elitist Greedy Randomized Adaptive Search Procedure (GRASP) metaheuristic algorithm, called mGRASP/MH, for approximating the Pareto-optimal front in the multi-objective quadratic assignment problem (mQAP). The proposed algorithm is characterized by three features: elite greedy randomized construction, adaptation of search directions and cooperation between solutions. The approach ...

We study different choices of search direction for primal-dual interior-point methods for semidefinite programming problems. One particular choice we consider comes from a specialization of a class of algorithms developed by Nesterov and Todd for certain convex programming problems. We discuss how the search directions for the Nesterov-Todd (NT) method can be computed efficiently and demonstrat...

We discuss several different search directions which can be used in primal-dual interior-point methods for semidefinite programming problems and investigate their theoretical properties, including scale invariance, primal-dual symmetry, and whether they always generate well-defined directions. Among the directions satisfying all but at most two of these desirable properties are the Alizadeh-Hae...

In order to approximate the set of Pareto optimal solutions, several evolutionary multi-objective optimization (EMO) algorithms transfer the multiobjective problem into several independent single-objective ones by means of scalarizing functions. The choice of the scalarizing functions’ underlying search directions, however, is typically problem-dependent and therefore difficult if no informatio...

This papers surveys different approaches to evaluation of web search summaries and describes experiments conducted at Yandex. We hypothesize that the complex task of snippet evaluation is best solved with a range of different methods. Automation of evaluation based on available manual assessments and clickthrough analysis is a promising direction.

One of the most promising trends in Domain-Independent AI Planning, nowadays, is state-space heuristic planning. The planners of this category construct general but efficient heuristic functions, which are used as a guide to traverse the state space either in a forward or in a backward direction. Although specific problems may favor one or the other direction, there is no clear evidence why any...