An improved SQP algorithm for solving minimax problems

AbstractIn this work, an improved SQP method is proposed for solving minimax problems, and a new method with small computational cost is proposed to avoid the Maratos effect. In addition, its global and superlinear convergence are obtained under some suitable conditions

A restricted memory quasi-Newton bundle method for nonsmooth optimization on Riemannian manifolds

In this paper, a restricted memory quasi-Newton bundle method for minimizing a locally Lipschitz function over a Riemannian manifold is proposed, which extends the classical one in Euclidean spaces to the manifold setting. The curvature information of the objective function is approximated by applying the Riemannian version of the quasi-Newton updating formulas. The subgradient aggregation technique is used to avoid solving the time-consuming quadratic programming subproblem when calculating the candidate descent direction. Moreover, a new Riemannian line search procedure is proposed to generate the stepsizes, and the process is finitely terminated under a new version of the Riemannian semismooth assumption. Global convergence of the proposed method is established: if the serious iteration steps are finite, then the last serious iterate is stationary; otherwise, every accumulation point of the serious iteration sequence is stationary. Finally, some preliminary numerical results show that the proposed method is efficient

A Partially Feasible Distributed SQO Method for Two-block General Linearly Constrained Smooth Optimization

This paper discusses a class of two-block smooth large-scale optimization problems with both linear equality and linear inequality constraints, which have a wide range of applications, such as economic power dispatch, data mining, signal processing, etc.Our goal is to develop a novel partially feasible distributed (PFD) sequential quadratic optimization (SQO) method (PFD-SQO method) for this kind of problems. The design of the method is based on the ideas of SQO method and augmented Lagrangian Jacobian splitting scheme as well as feasible direction method,which decomposes the quadratic optimization (QO) subproblem into two small-scale QOs that can be solved independently and parallelly. A novel disturbance contraction term that can be suitably adjusted is introduced into the inequality constraints so that the feasible step size along the search direction can be increased to 1. The new iteration points are generated by the Armijo line search and the partially augmented Lagrangian function that only contains equality constraints as the merit function. The iteration points always satisfy all the inequality constraints of the problem. The theoretical properties, such as global convergence, iterative complexity, superlinear and quadratic rates of convergence of the proposed PFD-SQO method are analyzed under appropriate assumptions, respectively. Finally, the numerical effectiveness of the method is tested on a class of academic examples and an economic power dispatch problem, which shows that the proposed method is quite promising

Study on the Self-Repairing Effect of Nanoclay in Powder Coatings for Corrosion Protection

Powder coatings are a promising, solvent-free alternative to traditional liquid coatings due to the superior corrosion protection they provide. This study investigates the effects of incorporating montmorillonite-based nanoclay additives with different particle sizes into polyester/triglycidyl isocyanurate (polyester/TGIC) powder coatings. The objective is to enhance the corrosion-protective function of the coatings while addressing the limitations of commonly employed epoxy-based coating systems that exhibit inferior UV resistance. The anti-corrosive and surface qualities of the coatings were evaluated via neutral salt spray tests, electrochemical measurements, and surface analytical techniques. Results show that the nanoclay with a larger particle size of 18.38 µm (D50, V) exhibits a better barrier effect at a lower dosage of 4%, while a high dosage leads to severe defects in the coating film. Interestingly, the coating capacitance is found, via electrochemical impedance spectroscopy, to decrease during the immersion test, indicating a self-repairing capability of the nanoclay, arising from its swelling and expansion. Neutral salt spray tests suggest an optimal nanoclay dosage of 2%, with the smaller particle size (8.64 µm, D50, V) nanoclay providing protection for 1.5 times as many salt spray hours as the nanoclay with a larger particle size. Overall, incorporating montmorillonite-based nanoclay additives is suggested to be a cost-effective approach for significantly enhancing the anti-corrosive function of powder coatings, expanding their application to outdoor environments

An alternating linearization bundle method for a class of nonconvex nonsmooth optimization problems

Abstract In this paper, we propose an alternating linearization bundle method for minimizing the sum of a nonconvex function and a convex function, both of which are not necessarily differentiable. The nonconvex function is first locally “convexified” by imposing a quadratic term, and then a cutting-planes model of the local convexification function is generated. The convex function is assumed to be “simple” in the sense that finding its proximal-like point is relatively easy. At each iteration, the method solves two subproblems in which the functions are alternately represented by the linearizations of the cutting-planes model and the convex objective function. It is proved that the sequence of iteration points converges to a stationary point. Numerical results show the good performance of the method

A QP-Free Algorithm for Finite Minimax Problems

The nonlinear minimax problems without constraints are discussed. Due to the expensive computation for solving QP subproblems with inequality constraints of SQP algorithms, in this paper, a QP-free algorithm which is also called sequential systems of linear equations algorithm is presented. At each iteration, only two systems of linear equations with the same coefficient matrix need to be solved, and the dimension of each subproblem is not of full dimension. The proposed algorithm does not need any penalty parameters and barrier parameters, and it has small computation cost. In addition, the parameters in the proposed algorithm are few, and the stability of the algorithm is well. Convergence property is described and some numerical results are provided

Convergence of Linear Bregman ADMM for Nonconvex and Nonsmooth Problems with Nonseparable Structure

The alternating direction method of multipliers (ADMM) is an effective method for solving two-block separable convex problems and its convergence is well understood. When either the involved number of blocks is more than two, or there is a nonconvex function, or there is a nonseparable structure, ADMM or its directly extend version may not converge. In this paper, we proposed an ADMM-based algorithm for nonconvex multiblock optimization problems with a nonseparable structure. We show that any cluster point of the iterative sequence generated by the proposed algorithm is a critical point, under mild condition. Furthermore, we establish the strong convergence of the whole sequence, under the condition that the potential function satisfies the Kurdyka–Łojasiewicz property. This provides the theoretical basis for the application of the proposed ADMM in the practice. Finally, we give some preliminary numerical results to show the effectiveness of the proposed algorithm