Search results for "Lagrange multiplier"
showing 10 items of 37 documents
Optimality Conditions for Non-Qualified Parabolic Control Problems
1994
We consider parabolic state constrained optimal control problems where the usual Slater condition is not necessarily satisfied. Instead, a weaker interiority property is assumed. Optimality conditions with a Lagrange multiplier are given. As an application we present an augmented Lagrangian algorithm. Numerical test results are included.
Nonradial normalized solutions for nonlinear scalar field equations
2018
We study the following nonlinear scalar field equation $$ -\Delta u=f(u)-\mu u, \quad u \in H^1(\mathbb{R}^N) \quad \text{with} \quad \|u\|^2_{L^2(\mathbb{R}^N)}=m. $$ Here $f\in C(\mathbb{R},\mathbb{R})$, $m>0$ is a given constant and $\mu\in\mathbb{R}$ is a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity $f$, we show the existence of one nonradial solution for any $N\geq4$, and obtain multiple (sometimes infinitely many) nonradial solutions when $N=4$ or $N\geq6$. In particular, all these solutions are sign-changing.
Analytic first derivatives for a spin-adapted open-shell coupled cluster theory: Evaluation of first-order electrical properties
2014
An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric open-shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for…
Constraint qualifications and Lagrange multipliers in nondifferentiable programming problems
1994
In this paper, we present several constraint qualifications, and we show that these conditions guarantee the nonvacuity and the boundedness of the Lagrange multiplier sets for general nondifferentiable programming problems. The relationships with various constraint qualifications are investigated.
On thermoeconomics of energy systems at variable load conditions: integrated optimization of plant design and operation
2007
Abstract Thermoeconomics has been assuming a growing role among the disciplines oriented to the analysis of energy systems, its different methodologies allowing solution of problems in the fields of cost accounting, plant design optimisation and diagnostic of malfunctions. However, the thermoeconomic methodologies as such are particularly appropriate to analyse large industrial systems at steady or quasi-steady operation, but they can be hardly applied to small to medium scale units operating in unsteady conditions to cover a variable energy demand. In this paper, the fundamentals of thermoeconomics for systems operated at variable load are discussed, examining the cost formation process an…
A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
2006
Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L^1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existe…
Numerical simulation of unsteady MHD flows and applications
2009
International audience; We present a robust numerical method for solving the compressible Ideal Magneto-Hydrodynamic equations. It is based on the Residual Distribution (RD) algorithms already successfully tested in many problems. We adapted the scheme to the multi-dimensional unsteady MHD model. The constraint ∇ · B = 0 is enforced by the use a Generalized Lagrange Multiplier (GLM) technique. First, we present this complete system and the keys to get its eigensystem, as we may need it in the algorithm. Next, we introduce the numerical scheme built in order to get a compressible, unsteady and implicit solver which has good shock-capturing properties and is second-order accurate at the conve…
Continuous spectrum for a two phase eigenvalue problem with an indefinite and unbounded potential
2020
Abstract We consider a two phase eigenvalue problem driven by the ( p , q ) -Laplacian plus an indefinite and unbounded potential, and Robin boundary condition. Using a modification of the Nehari manifold method, we show that there exists a nontrivial open interval I ⊆ R such that every λ ∈ I is an eigenvalue with positive eigenfunctions. When we impose additional regularity conditions on the potential function and the boundary coefficient, we show that we have smooth eigenfunctions.
Normalizing biproportional methods
2002
International audience; Biproportional methods are used to update matrices: the projection of a matrix Z to give it the column and row sums of another matrix is R Z S, where R and S are diagonal and secure the constraints of the problem (R and S have no signification at all because they are not identified). However, normalizing R or S generates important mathematical difficulties: it amounts to put constraints on Lagrange multipliers, non negativity (and so the existence of the solution) is not guaranteed at equilibrium or along the path to equilibrium.
Large eddy simulation of inertial particles dispersion in a turbulent gas-particle channel flow bounded by rough walls
2020
The purpose of this paper is to understand the capability and consistency of large eddy simulation (LES) in Eulerian–Lagrangian studies aimed at predicting inertial particle dispersion in turbulent wall-bounded flows, in the absence of ad hoc closure models in the Lagrangian equations of particle motion. The degree of improvement granted by LES models is object of debate, in terms of both accurate prediction of particle accumulation and local particle segregation; therefore, we assessed the accuracy in the prediction of the particle velocity statistics by comparison against direct numerical simulation (DNS) of a finer computational mesh, under both one-way and two-way coupling regimes. We p…