This paper proposes a generalized descent directions-guided multiobjective algorithm (DDMOA2). DDMOA2 uses the scalarizing fitness assignment in its parent and environmental selection procedures. The population consists of leader and non-leader individuals. Each individual in the population is represented by a tuple containing its genotype as well as the set of strategy parameters. The main nov...

This paper presents a descent direction method for finding extrema of locally Lipschitz functions defined on Riemannian manifolds. To this end we define a set-valued mapping x → ∂εf(x) named ε-subdifferential which is an approximation for the Clarke subdifferential and which generalizes the Goldstein-ε-subdifferential to the Riemannian setting. Using this notion we construct a steepest descent ...

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we pres...

The method of conjugate directions provides a very effective way to optimize large, deterministic systems by gradient descent. In its standard form, however, it is not amenable to stochastic approximation of the gradient. Here we explore ideas from conjugate gradient in the stochastic (online) setting, using fast Hessian-gradient products to set up low-dimensional Krylov subspaces within indivi...

Hybridization of local search based algorithms with evolutionary algorithms is still an under-explored research area in multiobjective optimization. In this paper, we propose a new multiobjective algorithm based on a local search method. The main idea is to generate new non-dominated solutions by adding a linear combination of descent directions of the objective functions to a parent solution ....

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,...

In this paper, we suggest and analyze a new iterative method for solving mixed quasi variational inequalities. The new iteration is obtained by searching the optimal step size along the integrated descent direction from two descent directions. Global convergence of the proposal method is proved under certain assumptions. Our results can be treated as refinement of previously known results. An e...

The aim of this paper is the study of different approaches to combine and scale, in an efficient manner, descent information for the solution of unconstrained optimization problems. We consider the situation in which different directions are available in a given iteration, and we wish to analyze how to combine these directions in order to provide a method more efficient and robust than the stan...

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [2] has driven us to consider a globalization strategy based on SD, which is applicable any line-search method. In particular, we combine Newton-type directions with scaled SD steps have suitable descent directions. Scaling step length makes significant difference respect similar approaches, terms b...