2026· Yugoslav journal of operations research· pp. 11-11· 0 citations
TL;DR
The concept of a regularized gap function is employed to reformulate the constrained problem into an unconstrained one and a positive definite Hessian modification along with a backtracking line search is incorporated to promote global convergence.
Abstract
In this paper, we propose an alternative approach to Sequential Quadratic Programming (SQP) for solving optimization problems with linear equality constraints. The concept of a regularized gap function is employed to reformulate the constrained problem into an unconstrained one. The proposed algorithm incorporates a positive definite Hessian modification along with a backtracking line search to promote global convergence. Its effectiveness is demonstrated through several numerical experiments and geometric illustrations. Furthermore, applications of the proposed method are explored in optimal allocation, analytic center computation, and network flow problems.
We study mixed-integer quadratic fractional optimization problems with binary and continuous box-constrained variables. The objective is the ratio of two quadratic functions, a structure that arises naturally in portfolio selection, signal processing, and data analytics. We propose an exact algorithm based on Dinkelbac...
Marco Locatelli, V. Piccialli, A. M. Sudoso· 0 citations
We give an approach for finding a global minimization with equality and inequality Constraints.Our approach is to construct an exact penalty function, and prove that the global minimal points of this exact penalty function are the primal constrained global minimal points. Thus we convert the problem of global constrain...
Lian-Sheng Zhang· Journal of Computational Mat...· 0 citations
Theoretical analysis confirms that these inexact variants of GRPDA retain the convergence properties of their exact counterparts, and they are applied to some total-variation-based image deblurring problems.
We consider a mathematical program with equilibrium constraints (MPEC). First we obtain a Lagrange multiplier rule based on the linear subdifferential involving equality, inequality and set constraints. Then we propose new constraint qualifications for M-stationary condition to hold. Finally we establish the Fritz John...
N. Movahedian, S. Nobakhtian· Journal of Convex Analysis· 0 citations
We consider nonconvex conic optimization that covers Standard Nonlinear Programming, Semidefinite Programming, Second Order Cone Programming. To the dual Lagrangian problem, we associate a relaxed primal convex problem, and give bounds for the duality gap. Then we propose a proximal extension of the column generation m...
A. Auslender· Journal of Convex Analysis· 0 citations
In this paper, a block coordinate descent method is developed to solve
a linearly constrained separable convex optimization problem. The proposed
method divides the decision variable into a few blocks based on certain rules.
Then the candidate solution is iteratively obtained by updating one block at
each iteration. Th...
Xue-Fang Liu, Zheng Peng· Annals of Applied Mathematic...· 0 citations
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