Related papers: A New Approach for Solving the Linear Complementar…
In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…
New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the…
It has been verified that the linear programming (LP) is able to formulate many real-life optimization problems, which can obtain the optimum by resorting to corresponding solvers such as OptVerse, Gurobi and CPLEX. In the past decades, a…
A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…
In practical engineering and optimization, solving multi-objective optimization (MOO) problems typically involves scalarization methods that convert a multi-objective problem into a single-objective one. While effective, these methods often…
Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the…
For several decades the dominant techniques for integer linear programming have been branching and cutting planes. Recently, several authors have developed core point methods for solving symmetric integer linear programs (ILPs). An integer…
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the…
Although a unique solution is guaranteed in the Linear complementarity problem (LCP) when the matrix $\mathbf{M}$ is positive definite, practical applications often involve cases where $\mathbf{M}$ is only positive semi-definite, leading to…
In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objective or constraints contain black-box functions only known at…
We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
The paper aims to show the equivalency between nonlinear complementarity problem and the system of nonlinear equations. We propose a homotopy method with vector parameter $\lambda$ in finding the solution of nonlinear complementarity…