Scholarlink

<p>It is known that the sequential quadratic programming (SQP) method and the alternating direction method of multipliers (ADMM) are two kinds of very effective tools for solving smooth small-to-medium-scale optimization and large-scale separable optimization, respectively. This paper discusses a class of large-scale two-block optimization problems with linear equality-inequality constraints, where the objective function is smooth but not necessarily convex. Our aim is to design a novel ADMM-SQP method based on the fully augmented Lagrangian function (FALF for short, namely, both the equality constraints and the inequality constraints are considered in the augmented Lagrangian function). The main technical routes are as follows. First, based on FALF technique, transform the quadratic programming (QP) subproblem associated with the original problem to a piecewise QP (PQP) subproblem with simple constraints. Second, use the Gauss-Seidel splitting to divide the PQP into two small-scale PQP subproblems. And then, by linearizing the piecewise quadratic objective, reduce the PQP subproblems to two standard QP subproblems, which can yield two improved search directions corresponding to the primal two-block variables. Third, with the FALF of the original problem as a merit function, along the improved search directions, execute Armijo line search to generate the new iteration point. Fourth, the multipliers are updated by a new scheme different from ADMM. Based on a key inequality established in this paper, the global convergence and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {O}(\varepsilon ^{-2})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo stretchy="false">(</mo> <msup> <mi>ε</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> iteration complexity of the proposed method can be obtained. Finally, a preliminary numerical test is carried out. To our knowledge, this is the first FALF-based method for equality-inequality constrained non-convex optimization.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An ADMM-SQP FALF-Based Method for Two-Block Nonconvex Optimization with Linear Equality-Inequality Constraints

  • 期刊论文

  • 发表日期：

    2026年7月1日

查看全文
  • Jin-Bao Jian,
  • Jing-Min Cai,
  • Jiang-Hua Yin,
  • Xian-Zhen Jiang,
  • Guo-Dong Ma

摘要

It is known that the sequential quadratic programming (SQP) method and the alternating direction method of multipliers (ADMM) are two kinds of very effective tools for solving smooth small-to-medium-scale optimization and large-scale separable optimization, respectively. This paper discusses a class of large-scale two-block optimization problems with linear equality-inequality constraints, where the objective function is smooth but not necessarily convex. Our aim is to design a novel ADMM-SQP method based on the fully augmented Lagrangian function (FALF for short, namely, both the equality constraints and the inequality constraints are considered in the augmented Lagrangian function). The main technical routes are as follows. First, based on FALF technique, transform the quadratic programming (QP) subproblem associated with the original problem to a piecewise QP (PQP) subproblem with simple constraints. Second, use the Gauss-Seidel splitting to divide the PQP into two small-scale PQP subproblems. And then, by linearizing the piecewise quadratic objective, reduce the PQP subproblems to two standard QP subproblems, which can yield two improved search directions corresponding to the primal two-block variables. Third, with the FALF of the original problem as a merit function, along the improved search directions, execute Armijo line search to generate the new iteration point. Fourth, the multipliers are updated by a new scheme different from ADMM. Based on a key inequality established in this paper, the global convergence and \(\mathcal {O}(\varepsilon ^{-2})\) O ( ε - 2 ) iteration complexity of the proposed method can be obtained. Finally, a preliminary numerical test is carried out. To our knowledge, this is the first FALF-based method for equality-inequality constrained non-convex optimization.