Related papers: Homotopy methods for higher order shape optimizati…
In this paper, we introduce a homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of two-person zero-sum discounted stochastic ARAT game. We show that the algorithm has the…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
Tuning step sizes is crucial for the stability and efficiency of optimization algorithms. While adaptive coordinate-wise step sizes have been shown to outperform scalar step size in first-order methods, their use in second-order methods is…
In this paper, we propose two second-order methods for solving the \(\ell_1\)-regularized composite optimization problem, which are developed based on two distinct definitions of approximate second-order stationary points. We introduce a…
We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…
Multiobjective optimization (MOO) is prevalent in numerous applications, in which a Pareto front (PF) is constructed to display optima under various preferences. Previous methods commonly utilize the set of Pareto objectives (particles on…
This paper addresses the challenge of dynamic multi-objective optimization problems (DMOPs) by introducing novel approaches for accelerating prediction strategies within the evolutionary algorithm framework. Since the objectives of DMOPs…
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…
Planning the motion for humanoid robots is a computationally-complex task due to the high dimensionality of the system. Thus, a common approach is to first plan in the low-dimensional space induced by the robot's feet---a task referred to…
This paper aims to develop a Newton-type method to solve a class of nonconvex composite programs. In particular, the nonsmooth part is possibly nonconvex. To tackle the nonconvexity, we develop a notion of strong prox-regularity which is…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
We propose a homotopy sampling procedure, loosely based on importance sampling. Starting from a known probability distribution, the homotopy procedure generates the unknown normalization of a target distribution. In the context of…
In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…
The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for…
In this work we propose a general nonmonotone line-search method for nonconvex multi\-objective optimization problems with convex constraints. At the $k$th iteration, the degree of nonmonotonicity is controlled by a vector $\nu_{k}$ with…
We present a general shape optimisation framework based on the method of mappings in the $W^{1,\infty}$ topology. We propose steepest descent and Newton-like minimisation algorithms for the numerical solution of the respective shape…
This paper deals with discrete topology optimization and describes the modification of a single-objective algorithm into its multi-objective counterpart. The result is a significant increase in the optimization speed and quality of the…
We extend the nonlocal operator method to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original nonlocal operator method proposed by the authors in [A…