The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are ...The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.展开更多
Background:Schistosomiasis is a parasitic disease.It is caused by a prevalent infection in tropical areas and is transmitted through contaminated water with larvae parasites.Schistosomiasis is the second most parasiti...Background:Schistosomiasis is a parasitic disease.It is caused by a prevalent infection in tropical areas and is transmitted through contaminated water with larvae parasites.Schistosomiasis is the second most parasitic disease globally,so investigating its prevention and treatment is crucial.Methods:This paper aims to suggest a time-fractional model of schistosomiasis disease(T-FMSD)in the sense of the Caputo operator.The T-FMSD considers the dynamics involving susceptible ones not infected with schistosomiasis(S_(h)(t)),those infected with the infection(Ih(t)),those recovering from the disease(R(t)),susceptible snails with and without schistosomiasis infection,respectively shown by I_(v)(t)and S_(v)(t).We use a new basis function,generalized Bernoulli polynomials,for the approximate solution of T-FMSD.The operational matrices are incorporated into the method of Lagrange multipliers so that the fractional problem can be transformed into an algebraic system of equations.Results:The existence and uniqueness of the solution,and the convergence analysis of the model are established.The numerical computations are graphically presented to depict the variations of the compartments with time for varied fractional order derivatives.Conclusions:The proposed method not only provides an accurate solution but also can accurately predict schistosomiasis transmission.The results of this study will assist medical scientists in taking necessary measures during screening and treatment processes.展开更多
文摘The Stackelberg prediction game(SPG)is a bilevel optimization frame-work for modeling strategic interactions between a learner and a follower.Existing meth-ods for solving this problem with general loss functions are computationally expensive and scarce.We propose a novel hyper-gradient type method with a warm-start strategy to address this challenge.Particularly,we first use a Taylor expansion-based approach to obtain a good initial point.Then we apply a hyper-gradient descent method with an ex-plicit approximate hyper-gradient.We establish the convergence results of our algorithm theoretically.Furthermore,when the follower employs the least squares loss function,our method is shown to reach an e-stationary point by solving quadratic subproblems.Numerical experiments show our algorithms are empirically orders of magnitude faster than the state-of-the-art.
文摘Background:Schistosomiasis is a parasitic disease.It is caused by a prevalent infection in tropical areas and is transmitted through contaminated water with larvae parasites.Schistosomiasis is the second most parasitic disease globally,so investigating its prevention and treatment is crucial.Methods:This paper aims to suggest a time-fractional model of schistosomiasis disease(T-FMSD)in the sense of the Caputo operator.The T-FMSD considers the dynamics involving susceptible ones not infected with schistosomiasis(S_(h)(t)),those infected with the infection(Ih(t)),those recovering from the disease(R(t)),susceptible snails with and without schistosomiasis infection,respectively shown by I_(v)(t)and S_(v)(t).We use a new basis function,generalized Bernoulli polynomials,for the approximate solution of T-FMSD.The operational matrices are incorporated into the method of Lagrange multipliers so that the fractional problem can be transformed into an algebraic system of equations.Results:The existence and uniqueness of the solution,and the convergence analysis of the model are established.The numerical computations are graphically presented to depict the variations of the compartments with time for varied fractional order derivatives.Conclusions:The proposed method not only provides an accurate solution but also can accurately predict schistosomiasis transmission.The results of this study will assist medical scientists in taking necessary measures during screening and treatment processes.
