We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, ...
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This paper presents a mathematical model for a photovoltaic hydrogen production system, along with an optimal design study applied to this system. Precise modeling of hydrogen production has proven to be a challenging...
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This paper presents a mathematical model for a photovoltaic hydrogen production system, along with an optimal design study applied to this system. Precise modeling of hydrogen production has proven to be a challenging task. Based on previous work, a general framework is proposed for battery pack-assisted photovoltaic hydrogen production. Specifically, explicit mathematical expressions are given for the hydrogen production efficiency of the electrolyzer, and a current source model is established for the photovoltaic panels. Regarding the optimal design, a systematic framework is outlined to obtain the optimal strategy by converting the control problem into a boundary value problem, subsequently solved via nonlinear programming. Simulation results show that under the optimal strategy, the battery energy consumption by the photovoltaic hydrogen production system is significantly reduced, while maintaining minimal power consumption operation when the irradiation is insufficient, without the need for frequent start-stop cycles. In addition, the calculation time of the IPOPT solver to find the optimal strategy is discussed, proving its ability to address nonlinear planning problems at a millisecond-level calculation time.
We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold...
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In this paper, we present a two phase method for solving nonlinear programming problems called nonlinear Polyhedral Active Set Algorithm (NPASA) that has global and local convergence guarantees under reasonable assump...
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This paper presents a new and efficient method, referred to as an aggregate constraint method, for the solution of general non-linear programming problems in which a multi-constrained problem is converted to one with ...
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This paper presents a new and efficient method, referred to as an aggregate constraint method, for the solution of general non-linear programming problems in which a multi-constrained problem is converted to one with a single parametric constraint. This is derived by using the two concepts of constraint surrogation and maximum entropy, and represents a uniform approximation to the original constraint set. An augmented Lagrangean algorithm is then used to solve the resulting problem. Numerical examples are given to show the high efficiency of the present method.
This study proposes an analytical Delta-V approximation of short-timetransfers based on the linear relative motion and a gradient-based nonlinear programming model of multi-target rendezvous and fly by trajectories. I...
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Localization is used in location-aware applications such as navigation, autonomous robotic movement, and asset tracking to position a moving object on a coordinate system. In this paper, a nonlinear programming algori...
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LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly eff...
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In this paper,we study the following nonlinear nonconvex programming problem:min f(x),***(x) ≤0,i ∈M,M={1,2,···,m}.Under the condition that the feasible set is bounded and connected,and the feasible s...
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In this paper,we study the following nonlinear nonconvex programming problem:min f(x),***(x) ≤0,i ∈M,M={1,2,···,m}.Under the condition that the feasible set is bounded and connected,and the feasible set does not satisfy the pseudonormal cone conditions,we propose the combined homotopy method to solve this problem by constructing new constraint functions and a combined homotopy *** convergence of the method is proved and the existence of a smooth homotopy path from any interior point to a solution of the problem is *** examples show that this method is feasible and effective.
The minimum norm Lagrange multiplier, as a type of informative Lagrange multiplier, is proposed to replace the classical shadow price when the later fails to exist. This kind of multiplier expresses the rate of cost i...
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The minimum norm Lagrange multiplier, as a type of informative Lagrange multiplier, is proposed to replace the classical shadow price when the later fails to exist. This kind of multiplier expresses the rate of cost improvement when the right-hand side of the constraints are permitted to slightly violated. However, the minimum norm Lagrange multiplier may fail to be informative in fully parametric optimization problems. In this paper, we extend the classical constraint violation condition to a general formulation, which captures the characteristics of the problem structure of nonlinear parametric programming models. Based on the generalized constraint violation condition, we provide sufficient conditions for the minimum norm Lagrange multiplier to be informative. Furthermore, we propose a kind of penalty function method to derive the informative Lagrange multiplier in fully parametric programming models, which means that the perturbations are not only on the right-hand side of the constraints. Finally, we use examples to support our theoretic results.
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