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On Types of Isolated KKT Points in Polynomial Optimization
Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in ℝ n . In this paper, the authors are interested in...
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KKT-based primal-dual exactness conditions for the Shor relaxation
In this work we present some exactness conditions for the Shor relaxation of diagonal (or, more generally, diagonalizable) QCQPs, which extend the...
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Approximations for Pareto and Proper Pareto solutions and their KKT conditions
In this article, we view the Pareto and weak Pareto solutions of the multiobjective optimization by using an approximate version of KKT type...
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A 2-Level Domain Decomposition Preconditioner for KKT Systems with Heat-Equation Constraints
This paper develops a new domain-decomposition method for solving the KKT system with heat-equation constraints.
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Infinite Programming and Application in the Best Proximity Point Theory
Various types of unconnected optimization problems in infinite space are explored. In particular, many papers have been published on the best...
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Accelerating Condensed Interior-Point Methods on SIMD/GPU Architectures
The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear...
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On approximate strong KKT points of nonsmooth interval-valued mutiobjective optimization problems using convexificators
The aim of this paper is to study interval-valued mutiobjective optimization problems involving inequality and set constraints. We derive...
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A preconditioned iterative interior point approach to the conic bundle subproblem
The conic bundle implementation of the spectral bundle method for large scale semidefinite programming solves in each iteration a semidefinite...
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An alternative extrapolation scheme of PDHGM for saddle point problem with nonlinear function
Primal-dual hybrid gradient (PDHG) method is a canonical and popular prototype for solving saddle point problem (SPP). However, the nonlinear...
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A primal-dual interior-point relaxation method with global and rapidly local convergence for nonlinear programs
Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel...
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Proximity measures based on KKT points for constrained multi-objective optimization
An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the...
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Solving Multiobjective Environmentally Friendly and Economically Feasible Electric Power Distribution Problem by Primal-Dual Interior-Point Method
This paper introduces a primal-dual interior-point algorithm to obtain the Pareto optimal solutions for a multiobjective environmentally friendly and...
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Riemannian Interior Point Methods for Constrained Optimization on Manifolds
We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior...
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Introduction to Interior Point Methods
In this chapter we give a short introduction to interior point methods (IPMs). We start from early results given in the 1960s on barrier methods and...
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A projected-search interior-point method for nonlinearly constrained optimization
This paper concerns the formulation and analysis of a new interior-point method for constrained optimization that combines a shifted primal-dual...
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A semismooth Newton based dual proximal point algorithm for maximum eigenvalue problem
The maximum eigenvalue problem is to minimize the maximum eigenvalue function over an affine subspace in a symmetric matrix space, which has many...
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Interior-Point Methods
One of the most powerful methods for solving nonlinear optimization problems known as the interior-point method is to be presented in this chapter....
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Local convergence of primal–dual interior point methods for nonlinear semidefinite optimization using the Monteiro–Tsuchiya family of search directions
The recent advance of algorithms for nonlinear semidefinite optimization problems (NSDPs) is remarkable. Yamashita et al. first proposed a...
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Complexity analysis of interior-point methods for second-order stationary points of nonlinear semidefinite optimization problems
We propose a primal-dual interior-point method (IPM) with convergence to second-order stationary points (SOSPs) of nonlinear semidefinite...
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A global interior point method for nonconvex geometric programming
The strategy presented in this paper differs significantly from existing approaches as we formulate the problem as a standard optimization problem of...
