arXiv subjects

Jinbao Jian

Publications and source records attributed to Jinbao Jian.

10 recordsLinked to original sources

arXiv2026

A globally and superlinearly convergent QO-free method for nonlinear optimization on Riemannian manifolds

The quadratic optimization-free (QO-free) method is a class of powerful and effective algorithms for solving nonlinearly constrained optimization problems in Euclidean spaces. The aim of the present work is to extend this method to solve optimization problems on manifolds with additional equality and inequality constraints. We first present a specific algorithm in the manifold setting. At each iteration, three linear systems sharing a common linear operator are solved to determine the master search direction. In addition, a higher-order correction direction is obtained by solving a reduced linear least squares subproblem to circumvent the Maratos effect which is assumed not to arise in existing related literature. A Riemannian arc search is then performed within the tangent space of the current iterate to generate the new iterate. Under appropriate assumptions, we establish the global and strong convergence of the proposed method. Moreover, we prove that the unit step size will eventually be accepted by the arc search, upon which the superlinear convergence of the algorithm is established. Finally, numerical results demonstrate that the proposed method is very competitive compared with other existing approaches.

math.OC↗

arXiv2026

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 continuous function over a Riemannian manifold is proposed. The curvature information of the objective function is approximated by applying a Riemannian version of the quasi-Newton updating formulas. A Riemannian subgradient aggregation technique is proposed and used to significantly reduce the computations in the quadratic programming subproblem when calculating the candidate descent direction. Moreover, a Riemannian line-search procedure is proposed to generate the stepsizes, and the process is finitely terminated under the assumption of a newly proposed Riemannian semismoothness. 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. In addition, a modified algorithm with limited-memory quasi-Newton updates is presented to further reduce the computational cost. Finally, numerical experiments demonstrate that (i) the quasi-Newton updates accelerate the convergence of the bundle method, (ii) the aggregation technique significantly reduces the computational cost for solving the quadratic programming subproblem, and (iii) the proposed methods outperform the compared state-of-the-art Riemannian optimization methods for locally Lipschitz continuous functions.

math.OC↗

arXiv2025

Solving Unit Commitment Problems with Graph Neural Network based Initial Commitment Prediction and Large Neighborhood Search

Unit commitment problem (UCP) is a critical component of power market decision-making. However, its computational complexity necessitates effi-cient solution methods. In this work we propose a framework to accelerate the solving process of the UCP, and the data collecting process for two dis-tinct graph neural network (GNN) policy. We at first train a Neural Initial Commitment Prediction policy to obtain an initial commitment for UCP. Sec-ond, a heuristic process is introduced to restore the feasibility of the initial commitment. Third, get the neighborhood based on the initial prediction then neighborhood search to improve the commitment. At last, we train a Neural neighborhood Prediction policy to predict the neighborhood of the incum-bent commitment at each iteration, continuously optimizing the commitment until the stopping condition is met. This approach produces high-quality ini-tial commitments that can be iteratively refined to meet higher accuracy re-quirements. The experimental results show that the GNN policies trained on the 80-unit system outperform commercial solvers on a 1080-unit system, and LNS performs better than commercial solver on more complex instanc-es.

math.OC↗

arXiv2025

An accelerated proximal PRS-SQP algorithm with dual ascent-descent procedures for smooth composite optimization

Conventional wisdom in composite optimization suggests augmented Lagrangian dual ascent (ALDA) in Peaceman-Rachford splitting (PRS) methods for dual feasibility. However, ALDA may fail when the primal iterate is a local minimum, a stationary point, or a coordinatewise solution of the highly nonconvex augmented Lagrangian function. Splitting sequential quadratic programming (SQP) methods utilize augmented Lagrangian dual descent (ALDD) to directly minimize the primal residual, circumventing the limitations of ALDA and achieving faster convergence in smooth optimization. This paper aims to present a fairly accessible generalization of two contrasting dual updates, ALDA and ALDD, for smooth composite optimization. A key feature of our PRS-SQP algorithm is its dual ascent-descent procedure, which provides a free direction rule for the dual updates and a new insight to explain the counterintuitive convergence behavior. Furthermore, we incorporate a hybrid acceleration technique that combines inertial extrapolation and back substitution to improve convergence. Theoretically, we establish the feasibility for a wider range of acceleration factors than previously known and derive convergence rates within the Kurdyka- Lojasiewicz framework. Numerical experiments validate the effectiveness and stability of the proposed method in various dual-update scenarios.

math.OC↗

arXiv2025

A descent method for nonsmooth multiobjective optimization problems on Riemannian manifolds

In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in existing methods. A necessary condition for Pareto optimality in Euclidean space is generalized to the Riemannian setting. At every iteration, an acceptable descent direction is obtained by constructing a convex hull of some Riemannian $\varepsilon$-subgradients. And then a Riemannian Armijo-type line search is executed to produce the next iterate. The convergence result is established in the sense that a point satisfying the necessary condition for Pareto optimality can be generated by the algorithm in a finite number of iterations. Finally, some preliminary numerical results are reported, which show that the proposed method is efficient.

math.OC↗

arXiv2023

Monotone Splitting SQP Algorithms for Two-block Nonconvex Optimization Problems with General Linear Constraints and Applications

In this work, based on the ideas of alternating direction method with multipliers (ADMM) and sequential quadratic programming (SQP), as well as Armijo line search technology, monotone splitting SQP algorithms for two-block nonconvex optimization problems with linear equality, inequality and box constraints are discussed. Firstly, the discussed problem is transformed into an optimization problem with only linear equality and box constraints by introducing slack variables. Secondly, we use the idea of ADMM to decompose the quadratic programming (QP) subproblem. Especially, the QP subproblem corresponding to the introducing slack variable is simple, and it has an explicit optimal solution without increasing computational cost. Thirdly, the search direction is generated by the optimal solutions of the subproblems, and the new iteration point is yielded by Armijo line search with augmented Lagrange function. And the global convergence of the algorithm is analyzed under weaker assumptions. In addition, box constraints are extended to general nonempty closed convex sets, moreover, the global convergence of the corresponding algorithm is also proved. Finally, some preliminary numerical experiments and applications in the mid-to-large-scale economic dispatch problems for power systems are reported, and these show that our proposed algorithm is promising.

math.OC↗

arXiv2017

Solution to dynamic economic dispatch with prohibited operating zones via MILP

Dynamic economic dispatch (DED) problem considering prohibited operating zones (POZ), ramp rate constraints, transmission losses and spinning reserve constraints is a complicated non-linear problem which is difficult to solve efficiently. In this paper, a mixed integer linear programming (MILP) method is proposed to solve such a DED problem. Firstly, a novel MILP formulation for DED problem without considering the transmission losses, denoted by MILP-1, is presented by using perspective cut reformulation technique. When the transmission losses are considered, the quadratic terms in the transmission losses are replaced by their first order Taylor expansions, and then an MILP formulation for DED considering the transmission losses, denoted by MILP-2, is obtained. Based on MILP-1 and MILP-2, an MILP-iteration algorithm (MILP-IA) is proposed to solve the complicated DED problem. The effectiveness of the MILP-1 and MILP-IA are assessed by several cases and the simulation results show that both of them can solve to competitive solutions in a short time.

math.OC↗

arXiv2017

A Hybrid MILP and IPM for Dynamic Economic Dispatch with Valve Point Effect

Dynamic economic dispatch with valve-point effect (DED-VPE) is a non-convex and non-differentiable optimization problem which is difficult to solve efficiently. In this paper, a hybrid mixed integer linear programming (MILP) and interior point method (IPM), denoted by MILP-IPM, is proposed to solve such a DED-VPE problem, where the complicated transmission loss is also included. Due to the non-differentiable characteristic of DED-VPE, the classical derivative-based optimization methods can not be used any more. With the help of model reformulation, a differentiable non-linear programming (NLP) formulation which can be directly solved by IPM is derived. However, if the DED-VPE is solved by IPM in a single step, the optimization will easily trap in a poor local optima due to its non-convex and multiple local minima characteristics. To exploit a better solution, an MILP method is required to solve the DED-VPE without transmission loss, yielding a good initial point for IPM to improve the quality of the solution. Simulation results demonstrate the validity and effectiveness of the proposed MILP-IPM in solving DED-VPE.

math.OC↗

arXiv2017

A Mixed Integer Linear Programming Method for Dynamic Economic Dispatch with Valve Point Effect

In this paper, a mixed integer linear programming (MILP) formulation is proposed to solve the dynamic economic dispatch with valve-point effect (DED-VPE). Based on piecewise linearization technique, the non-convex and non-smooth generation cost is reformulated into a linear lower approximation which is better than the quadratic one, yielding an MILP formulation for the DED-VPE. When the segment parameter is set appropriately, the MILP formulation can be solved by a mixed integer programming (MIP) solver directly and efficiently. Thus, a global optimal solution within a preset tolerance can be guaranteed for the MILP formulation. Simulation results show that the proposed MILP formulation can be solved to reliable solutions in reasonable time.

math.OC↗

arXiv2017

A Novel Projected Two Binary Variables Formulation for Unit Commitment Problem

The thermal unit commitment (UC) problem often can be formulated as a mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. In this paper, with projecting unit generation level onto [0,1] and reformulation techniques, a novel two binary (2-bin) variables MIQP formulation for UC problem is presented. We show that 2-bin formulation is more compact than the state-of-the-art one binary (1-bin) variable formulation and three binary (3-bin) variables formulation. Moreover, 2-bin formulation is tighter than 1-bin and 3-bin formulations in quadratic cost function, and it is tighter than 1-bin formulation in linear constraints. Three mixed integer linear programming (MILP) formulations can be obtained from three UC MIQPs by replacing the quadratic terms in the objective functions by a sequence of piece-wise perspective-cuts. 2-bin MILP is also the best one due to the similar reasons of MIQP. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 hours show that the proposed 2-bin formulations are competitive with currently state-of-the-art formulations and promising for large-scale UC problems.

math.OC↗