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Distributionally robust shortfall risk portfolio model with moment ambiguity sets
Yi Yang, Liu Yang, Suhan Zhong
This paper employs shortfall risk to measure portfolio risk. Assume stock returns follow polynomial relations with their influence factors. We propose a moment-based distributional…
Sparse Copositive Polynomial Optimization
Suhan Zhong, Jinling Zhou, Jiawang Nie +1
This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS re…
Log-Polynomial Optimization
Jiyoung Choi, Jiawang Nie, Xindong Tang +1
We study an optimization problem in which the objective is given as a sum of logarithmic-polynomial functions. This formulation is motivated by statistical estimation principles su…
Moment Relaxations for Data-Driven Wasserstein Distributionally Robust Optimization
Shixuan Zhang, Suhan Zhong
We propose moment relaxations for data-driven -Wasserstein distributionally robust optimization (-WDRO) problems that are defined by polynomials. The proposed moment relaxati…
A global approach for generalized semi-infinte programs with polyhedral parameter sets
Xiaomeng Hu, Jiawang Nie, Suhan Zhong
This paper studies generalized semi-infinite programs (GSIPs) defined with polyhedral parameter sets. Assume these GSIPs are given by polynomials. We propose a new approach to solv…
Generalized Nash equilibrium problems with quasi-linear constraints
Jiyoung Choi, Jiawang Nie, Xindong Tang +1
We study generalized Nash equilibrium problems (GNEPs) such that objectives are polynomial functions, and each player's constraints are linear in their own strategy. For such GNEPs…
A New Working Set Method for Nonlinear Inequality Constrained Minimization
Suhan Zhong, Jianxin Zhou
The main purpose of this project is to develop a new active set method (ASM) called a working set method (WSM) for solving a general nonlinear inequality constrained minimization p…
Towards Global Solutions for Nonconvex Two-Stage Stochastic Programs: A Polynomial Lower Approximation Approach
Suhan Zhong, Ying Cui, Jiawang Nie
This paper tackles the challenging problem of finding global optimal solutions for two-stage stochastic programs with continuous decision variables and nonconvex recourse functions…
Distributionally Robust Optimization with Polynomial Robust Constraints
Jiawang Nie, Suhan Zhong
This paper studies distributionally robust optimization (DRO) with polynomial robust constraints. We give a Moment-SOS relaxation approach to solve the DRO. This reduces to solving…
Partial Lagrange Multiplier Expressions and Disjunctive Decompositions for Bilevel Optimization
Jiawang Nie, Jane J. Ye, Suhan Zhong
This paper studies bilevel polynomial optimization in which lower-level constraint functions depend linearly on lower-level variables. We show that such bilevel program can be refo…
Robust approximation of chance constrained optimization with polynomial perturbation
Bo Rao, Liu Yang, Suhan Zhong +1
This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint t…
Global optimization for the portfolio selection model with high-order moments
Liu Yang, Yi Yang, Suhan Zhong
In this paper, we study the global optimality of polynomial portfolio optimization (PPO). The PPO is a kind of portfolio selection model with high-order moments and flexible risk p…
Dehomogenization for Completely Positive Tensors
Jiawang Nie, Xindong Tang, Zi Yang +1
A real symmetric tensor is completely positive (CP) if it is a sum of symmetric tensor powers of nonnegative vectors. We propose a dehomogenization approach for studying CP tensors…
Loss Functions for Finite Sets
Jiawang Nie, Suhan Zhong
This paper studies loss functions for finite sets. For a given finite set , we give sum-of-square type loss functions of minimum degree. When is the vertex set of a standard…
Rational Generalized Nash Equilibrium Problems
Jiawang Nie, Xindong Tang, Suhan Zhong
This paper studies generalized Nash equilibrium problems that are given by rational functions. The optimization problems are not assumed to be convex. Rational expressions for Lagr…
Distributionally Robust Optimization with Moment Ambiguity Sets
Jiawang Nie, Liu Yang, Suhan Zhong +1
This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for the distributions. The objective and constraints are given by polynomia…
A Lagrange Multiplier Expression Method for Bilevel Polynomial Optimization
Jiawang Nie, Li Wang, Jane Ye +1
This paper studies bilevel polynomial optimization problems. To solve them, we give a method based on polynomial optimization relaxations. Each relaxation is obtained from the Kura…
Stochastic Polynomial Optimization
Jiawang Nie, Liu Yang, Suhan Zhong
This paper studies stochastic optimization problems with polynomials. We propose an optimization model with sample averages and perturbations. The Lasserre type Moment-SOS relaxati…