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Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization...
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Second-order KKT optimality conditions for multiobjective discrete optimal control problems
This paper deals with second-order necessary and sufficient optimality conditions of Karush–Kuhn–Tucker-type for local optimal solutions in the sense...
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On scaled stop** criteria for a safeguarded augmented Lagrangian method with theoretical guarantees
This paper discusses the use of a stop** criterion based on the scaling of the Karush–Kuhn–Tucker (KKT) conditions by the norm of the approximate...
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First- and Second-Order Optimality Conditions for Quadratically Constrained Quadratic Programming Problems
We consider a quadratic programming problem with quadratic cone constraints and an additional geometric constraint. Under suitable assumptions, we...
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Complexity of an inexact proximal-point penalty method for constrained smooth non-convex optimization
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex,...
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A new global algorithm for factor-risk-constrained mean-variance portfolio selection
We consider the factor-risk-constrained mean-variance portfolio-selection (MVPS) problem that allows managers to construct portfolios with desired...
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Inequality constrained stochastic nonlinear optimization via active-set sequential quadratic programming
We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous...
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Maximizing sum of coupled traces with applications
This paper concerns maximizing the sum of coupled traces of quadratic and linear matrix forms. The coupling comes from requiring the matrix variables...
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Some results on the filter method for nonlinear complementary problems
Recent studies show that the filter method has good numerical performance for nonlinear complementary problems (NCPs). Their approach is to...
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Robust optimality conditions for semi-infinite equilibrium problems involving data uncertainty
In this paper, we have first formulated semi-infinite equilibrium problems involving data uncertainty. For this class of problems, we have proposed...
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Projected orthogonal vectors in two-dimensional search interior point algorithms for linear programming
The vast majority of linear programming interior point algorithms successively move from an interior solution to an improved interior solution by...
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Optimality conditions for nonlinear optimization problems with interval-valued objective function in admissible orders
This paper addresses the optimization problems with interval-valued objective function. We consider three types of total order relationships on the...
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An inexact regularized proximal Newton method for nonconvex and nonsmooth optimization
This paper focuses on the minimization of a sum of a twice continuously differentiable function f and a nonsmooth convex function. An inexact...
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Stochastic first-order methods for convex and nonconvex functional constrained optimization
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential...
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Miscellaneous
This last chapter addresses several issues related to the previous chapters. The first part is mainly aimed at deriving optimality conditions for a...
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Sparse and risk diversification portfolio selection
Portfolio risk management has become more important since some unpredictable factors, such as the 2008 financial crisis and the recent COVID-19...
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Adaptive Finite Element Method for Dirichlet Boundary Control of Elliptic Partial Differential Equations
In this paper, we consider the Dirichlet boundary control problem of elliptic partial differential equations, and get a coupling system of the state...
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An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming
An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization...
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