A modified Polak-Ribière-Polyak conjugate gradient algorithm which satisfies both the sufficient descent condition and the conjugacy condition is presented. These properties are independent of the line search. The algorithms use the standard Wolfe line search. Under standard assumptions we show the global convergence of the algorithm. Numerical comparisons with conjugate gradient algorithms usi...

This paper investigates the minimization problem of weighted roundoff noise and pole sensitivity subject to l2-scaling constraints for state-space digital filters. A new measure for evaluating roundoff noise and pole sensitivity is proposed, and an efficient technique for minimizing this measure is developed. It is shown that the problem can be converted into an unconstrained optimization probl...

In this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a non...

Tensor methods for unconstrained optimization were rst introduced by Schn-abel and Chow SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate-size problems. The major contribution of this paper is the extension of these methods to large, sparse unconstrained optimization problems. This extension requires an entirely new way of solving the tensor model th...

we propose a novel hybrid algorithm named ACO-FA, which integrates the merits of ant colony optimization (ACO) with firefly algorithm (FA) to solve unconstrained optimization problems. The main feature of the hybrid algorithm is to hybridize the solution construction mechanism of the ACO with the FA. In our hybrid algorithm, the initial solutions are generated randomly from the search space, an...

We propose an optimal control approach to tackle large scale unconstrained optimization problems. Our discussion begins with the introduction of a new framework to describe and deene the structure of a general function with a large number of variables. Based on the new concepts, a suucient condition is established so that any large scale unconstrained optimization problem satisfying this suucie...

This paper describes a novel algorithm for numerical optimization, called Simple Adaptive Climbing (SAC). SAC is a simple efficient single-point approach that does not require a careful fine-tunning of its two parameters. SAC algorithm shares many similarities with local optimization heuristics, such as random walk, gradient descent, and hill-climbing. SAC has a restarting mechanism, and a powe...

We design and analyze minimax-optimal algorithms for online linear optimization games where the player’s choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark strategy. While the standard benchmark is the loss of the best strategy chosen from a bounded comparator set, we consider a very broad range of benchmark funct...

UOBYQA is a new algorithm for general unconstrained optimization calculations, that takes account of the curvature of the objective function, F say, by forming quadratic models by interpolation. Therefore, because no rst derivatives are required, each model is deened by 1 2 (n+1)(n+2) values of F, where n is the number of variables, and the interpolation points must have the property that no no...