A revised sequential quadratic semidefinite programming method for nonlinear semidefinite optimization

نویسندگان

چکیده

In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite programming (SQSDP) method for solving, in particular, degenerate nonlinear optimization problems. The algorithm is shown to converge globally without constraint qualification, it has some nice properties, including the feasible subproblems, their possible inexact computations. convergence was established approximate-Karush-Kuhn-Tucker (AKKT) trace-AKKT conditions, which are two optimality conditions conic contexts. However, recently, complementarity-AKKT (CAKKT) were also considered, as an alternative previous mentioned ones, that more practical. Since few methods CAKKT points, at least optimization, complete study associated SQSDP, here we propose revised version of method, maintaining good properties. We modify algorithm, prove global sense CAKKT, show preliminary numerical experiments.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Semidefinite Optimization Approach to Quadratic Fractional Optimization with a Strictly Convex Quadratic Constraint

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...

متن کامل

Complex Quadratic Optimization and Semidefinite Programming

In this paper we study the approximation algorithms for a class of discrete quadratic optimization problems in the Hermitian complex form. A special case of the problem that we study corresponds to the max-3-cut model used in a recent paper of Goemans and Williamson. We first develop a closed-form formula to compute the probability of a complex-valued normally distributed bivariate random vecto...

متن کامل

A sensitivity result for quadratic semidefinite programs with an application to a sequential quadratic semidefinite programming algorithm

In this short note a sensitivity result for quadratic semidefinite programming is presented under a weak form of second order sufficient condition. Based on this result, also the local convergence of a sequential quadratic semidefinite programming algorithm extends to this weak second order sufficient condition. Mathematical subject classification: 90C22, 90C30, 90C31, 90C55.

متن کامل

A Semidefinite Programming Method for Integer Convex Quadratic Minimization

We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice Z. We present a semidefinite programming (SDP) method for obtaining a nontrivial lower bound on the optimal value of the problem. By interpreting the solution to the SDP relaxation probabilistically, we obtain a randomized algorithm for finding good suboptimal solutions. The effectiveness of the m...

متن کامل

An inexact spectral bundle method for convex quadratic semidefinite programming

We present an inexact spectral bundle method for solving convex quadratic semidefinite optimization problems. This method is a first-order method, hence requires much less computational cost each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we solve an eigenvalue minimization problem inexactly, and solve a small convex quadratic semidef...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Industrial and Management Optimization

سال: 2023

ISSN: ['1547-5816', '1553-166X']

DOI: https://doi.org/10.3934/jimo.2023019