In this paper, a new hybrid conjugate gradient algorithm is proposed for solving unconstrained optimization problems. This new method can generate sufficient descent directions unrelated to any line search. Moreover, the global convergence of the proposed method is proved under the Wolfe line search. Numerical experiments are also presented to show the efficiency of the proposed algorithm, espe...

Using search directions of a recent class of three--term conjugate gradient methods, modified versions of the Hestenes-Stiefel and Polak-Ribiere-Polyak methods are proposed which satisfy the sufficient descent condition. The methods are shown to be globally convergent when the line search fulfills the (strong) Wolfe conditions. Numerical experiments are done on a set of CUTEr unconstrained opti...

‎based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified polak-ribière-polyak conjugate‎ ‎gradient method proposed by yu et al‎. ‎is presented‎.

We present a novel learning-based method for generating optimal motion plans for high-dimensional motion planning problems. In order to cope with the curse of dimensionality, our method proceeds in a fashion similar to block coordinate descent in finite-dimensional optimization: at each iteration, the motion is optimized over a lower dimensional subspace while leaving the path fixed along the o...

The effectiveness of Newton’s method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton methods for the nonconvex case. Line search modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certa...

This paper explores the existence of affine invariant descent directions for unconstrained minimization. While there may exist several affine invariant descent directions for smooth functions f at a given point, it is shown that for quadratic functions there exists exactly one invariant descent direction in the strictly convex case and generally none in the nondegenerate indefinite case. These ...

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 few years ago, the authors proposed a nature-inspired metaheuristic concept, the spiral optimization algorithm, which was inspired by spiral phenomena in nature. The principal idea of the algorithm is to utilize spiral trajectories generated by multiple generalized spiral models for search applications. The generalized spiral model is composed of a spiral matrix defined by a composite rotatio...

In this work we investigate a technique for accelerating convergence of adjoint–based optimization of PDE systems based on a nonlinear change of variables in the control space. This change of variables is accomplished in the differentiate–then–discretize approach by constructing the descent directions in a control space not equipped with the Hilbert structure. We show how such descent direction...