Lei Guo

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Verified

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• PhD
• Professor at East China University of Science and Technology

We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of t...

This paper studies stability for parametric mathematical programs with geometric constraints. We show that, under the no nonzero abnormal multiplier constraint qualification and the second-order growth condition or second-order sufficient condition, the locally optimal solution mapping and stationary point mapping are nonempty-valued and continuous...

This paper introduces and studies the optimal control problem with equilibrium constraints (OCPEC). The OCPEC is an optimal control problem with a mixed state and control equilibrium constraint formulated as a complementarity constraint and it can be seen as a dynamic mathematical program with equilibrium constraints. It provides a powerful modelin...

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) st...

When the objective function is not locally Lipschitz, constraint qualifications are no longer sufficient for Karush-Kuhn-Tucker (KKT) conditions to hold at a local minimizer, let alone ensuring an exact penalization. In this paper, we extend quasi-normality and relaxed constant positive linear dependence (RCPLD) condition to allow the non-Lipschitz...

The continuous network design problem (CNDP) has been recognized as one of the most challenging issues in the field of transportation. Existing approaches to solving the CNDP are primarily heuristic without convergence guarantee or suitable for handling small networks because of the inherent nonconvexity arising from its bilevel hierarchical struct...

This repository contains the software and data used in the paper A Penalized Sequential Convex Programming Approach for Continuous Network Design Problems. The primary goal of this work is to propose and evaluate a novel approach to solving continuous network design problems (CNDP), specifically through a penalized sequential convex programming met...

The second-best congestion pricing (SBCP) problem is one of the most challenging problems in transportation because of its two-level hierarchical structure. In spite of various intriguing attempts at solving SBCP, existing solution methods are either heuristic without a convergence guarantee or suitable for solving SBCP on small networks only. In t...

he second-best congestion pricing (SBCP) problem is one of the most challenging problems in transportation due to its two-level hierarchical structure. In spite of various intriguing attempts for solving SBCP, existing solution methods are either heuristic without convergence guarantee or suitable for solving SBCP on small networks only. In this pa...

Combinatorial bilevel congestion pricing (CBCP), a variant of the discrete network design problem, seeks to minimize the total travel time experienced by all travelers in a road network, by strategically selecting toll locations and determining the corresponding charges. Conventional wisdom suggests that these problems are intractable since they ha...

We consider how to solve a class of non-Lipschitz mathematical programs with equilibrium constraints (MPEC) where the objective function involves a non-Lipschitz sparsity-inducing function and other functions are smooth. Solving the non-Lipschitz MPEC is highly challenging since the standard constraint qualifications fail due to the existence of eq...

In this paper, we perform a sensitivity analysis for the maximal value function, which is the optimal value function for a parametric maximization problem. Our aim is to study various subdifferentials for the maximal value function. We obtain upper estimates of Fréchet, limiting, and horizon subdifferentials of the maximal value function by using s...

In this paper, we perform sensitivity analysis for the maximal value function which is the optimal value function for a parametric maximization problem. Our aim is to study various subdifferentials for the maximal value function. We obtain upper estimates of Fr\'{e}chet, limiting, and horizon subdifferentials of the maximal value function by using...

Multi-national corporations (MNCs) face a challenge to avoid supply chain disruption risks due to increasing social and environmental responsibility (SER) violations by their low-tier (the second- and lower-tier) suppliers. Based on observation of emerging collaborations between MNCs and NGOs in practice, we extend traditional contract-based risk m...

The command-and-control regulation is likely inefficient and costly. This study investigates a regional pollution control scheme with tax (RPCST) under which the central government sets the tax rate under a given pollutant reduction quota and local governments determine their pollution removal rates based on the central government’s policy. First,...

The mathematical program with switching constraints (MPSC), which has been introduced recently, is a difficult class of optimization problems since standard constraint qualifications are very likely to fail at local minimizers. Due to the failure of standard constraint qualifications, it is reasonable to propose some constraint qualifications for l...

Trunk-sharing (TS), a nascent ride-sharing (RS)-based crowdsourced delivery service, has been reshaping the pattern of urban logistics and the spatial distribution of urban traffic congestion. However, it is not yet clear how RS and TS interact and affect the urban traffic system. To this end, a link-node-based user equilibrium model -is proposed t...

The mathematical program with switching constraints (MPSC) is a kind of problems with disjunctive constraints. The existing convergence results cannot directly be applied to this kind of problem since the required constraint qualifications for ensuring the convergence are very likely to fail. In this paper, we apply the augmented Lagrangian method...

We propose a new augmented Lagrangian (AL) method for solving the mathematical program with complementarity constraints (MPCC), where the complementarity constraints are left out of the AL function and treated directly. Two observations motivate us to propose this method: The AL subproblems are closer to the original problem in terms of the constra...

With the proliferation of smartphone-based ridesharing apps around the world, traffic assignment with ridesharing is drawing increasing attention in recent years. A number of ridesharing user equilibrium (RUE) models have been proposed, but most of them are formulated as path-based mixed complementarity problems based on presumed ridesharing price...

We propose a new augmented Lagrangian (AL) method for solving the mathematical program with complementarity constraints (MPCC), where the complementarity constraints are left out of the AL function and treated directly. Two observations motivate us to propose this method: the AL subproblems are closer to the original problem in terms of the constra...

This paper considers a class of mathematical programs that include multiobjective generalized Nash equilibrium problems in the constraints. Little research can be found in the literature although it has some interesting applications. We present a single level reformulation for this kind of problems and show their equivalence in terms of global and...

In this paper, we consider the dual formulation of minimizing $\sum_{i\in I}f_i(x_i)+\sum_{j\in J} g_j(\mathcal{A}_jx)$ with the index sets $I$ and $J$ being large. To address the difficulties from the high dimension of the variable $x$ (i.e., $I$ is large) and the large number of component functions $g_j$ (i.e., $J$ is large), we propose a hybrid...

We introduce a unified algorithmic framework, called the proximal-like in-cremental aggregated gradient (PLIAG) method, for minimizing the sum of a convex function that consists of additive relatively smooth convex components and a proper lower semicontinuous convex regularization function over an abstract feasible set whose geometry can be capture...

We consider a class of mathematical programs with complementarity constraints (MPCC) where the objective function involves a non-Lipschitz sparsity-inducing term. Due to the existence of the non-Lipschitz term, existing constraint qualifications for locally Lipschitz MPCC cannot ensure that necessary optimality conditions hold at a local minimizer....

This paper considers the mathematical programs with equilibrium constraints (MPEC). It is well-known that, due to the existence of equilibrium constraints, the Mangasarian-Fromovitz constraint qualification does not hold at any feasible point of MPEC and hence, in general, the developed numerical algorithms for standard nonlinear programming proble...

As the main air pollution control pattern used in China, the independent emission reduction (IER) model mandated that each province reduce its air pollutant independently. Under this model, provinces paid huge pollutant removal costs because they could not select the optimal pollutant removal rate based on their emission reduction capacity and thei...

We introduce a unified algorithmic framework, called proximal-like incremental aggregated gradient (PLIAG) method, for minimizing the sum of a convex function that consists of additive relatively smooth convex components and a proper lower semi-continuous convex regularization function, over an abstract feasible set whose geometry can be captured b...

When the objective function is not locally Lipschitz, constraint qualifications are no longer sufficient for Karush-Kuhn-Tucker (KKT) conditions to hold at a local minimizer, let alone ensuring an exact penalization. In this paper, we extend quasi-normality and relaxed constant positive linear dependence (RCPLD) condition to allow the non-Lipschitz...

This paper focuses on the single-level reformulation of mixed integer bilevel programming problems (MIBLPP). Due to the existence of lower-level integer variables, the popular approaches in the literature such as the first-order approach are not applicable to the MIBLPP. In this paper, we reformulate the MIBLPP as a mixed integer mathematical progr...

This paper considers an EPEC (equilibrium program with equilibrium constraints) model for a competition problem in electricity markets. By making use of some potential functions, we propose an MPEC (mathematical program with equilibrium constraints) reformulation and show that the normalized Nash stationary points of the EPEC model are actually the...

This paper aims at developing effective numerical methods for solving mathematical programs with equilibrium constraints. Due to the existence of complementarity constraints, the usual constraint qualifications do not hold at any feasible point, and there are various stationarity concepts such as Clarke, Mordukhovich, and strong stationarities that...

In this paper, we focus on some new constraint qualifications introduced for nonlinear extremum problems in the recent literature. We show that, if the constraint functions are continuously differentiable, the relaxed Mangasarian–Fromovitz constraint qualification (or, equivalently, the constant rank of the subspace component condition) implies the...

In this paper, we perform sensitivity analysis of the value function for parametric mathematical programs with equilibrium constraints (MPEC). We show that the value function is directionally differentiable in every direction under the MPEC relaxed constant rank regularity condition, the MPEC no nonzero abnormal multiplier constraint qualification,...

This paper focuses on solving various stationarity systems for some kind of equilibrium programs with equilibrium constraints (EPEC). Since the popular stationarity systems for EPECs involve some unknown index sets, we first reformulate these stationarity systems as constrained equations and then we propose a globally and superlinearly convergent a...

The purpose of the paper is to develop globally convergent algorithms for solving the popular stationarity systems for mathematical programs with complementarity constraints (MPCC) directly. Since the popular stationarity systems for MPCC contain some unknown index sets, we first present some nonsmooth reformulations for the stationarity systems by...

We study the constraint qualifications for mathematical programs with equilibrium constraints (MPEC). Firstly, we investigate the weakest constraint qualifications for the Bouligand and Mordukhovich stationarities for MPEC. Then, we show that the MPEC relaxed constant positive linear dependence condition can ensure any locally optimal solution to b...

In this paper we study the mathematical program with geometric constraints such that the image of a mapping from a Banach space is included in a nonempty and closed subset of a finite dimensional space. We obtain the nonsmooth enhanced Fritz John necessary optimality conditions in terms of the approximate subdifferential. In the case where the Bana...