In this paper, the problem of finding a generalized Nash equilibrium (GNE) of a networked game is studied. Players are only able to choose their decisions from a feasible action set. The feasible set is considered to be a private linear equality constraint that is coupled through decisions of the other players. We consider that each player has his own private constraint and it has not to be sha...

We discuss a recently proposed method of quantizing general non-Lagrangian gauge theories. The method can be implemented in many different ways, in particular, it can employ a conversion procedure that turns an original non-Lagrangian field theory in d dimensions into an equivalent Lagrangian, topological field theory in d+1 dimensions. The method involves, besides the classical equations of mo...

We present an alternating direction method based on an augmented Lagrangian framework for solving semidefinite programming (SDP) problems in standard form. At each iteration, the algorithm, also known as a two-splitting scheme, minimizes the dual augmented Lagrangian function sequentially with respect to the Lagrange multipliers corresponding to the linear constraints, then the dual slack varia...

For a quadratic optimization problem (QOP) with linear equality constraints in continuous nonnegative variables and binary variables, we propose three relaxations in simplified forms with a parameter λ: Lagrangian, completely positive, and copositive relaxations. These relaxations are obtained by reducing the QOP to an equivalent QOP with a single quadratic equality constraint in nonnegative va...

Due to its relatively high total energy eeciency, the application of cogeneration is attracting increased attention. Today cogeneration is an essential element in the energy supply system in many countries, and when environmental and economic aspects are considered too, it seems to be a relevant option in expansion planning in many situations. The present paper presents a quite general and yet ...

Lagrangian relaxation has been pursued as a pertinent methodology for many hard scheduling problems. From standard duality theory, the method is known to provide good-quality bounds to the performance of the optimal solutions of these problems, and in certain cases, the optimal Lagrange multipliers can function as a starting point for the construction good suboptimal solutions for the original ...

The numerical methods of total variation (TV) model for image denoising, especially Rudin–Osher– Fatemi (ROF) model, is widely studied in the literature. However, the S 1 constrained counterpart is less addressed. The classical gradient descent method for the constrained problem is limited in two aspects: one is the small time step size to ensure stability; the other is that the data must be pr...

For a quadratic optimization problem (QOP) with linear equality constraints in continuous nonnegative variables and binary variables, we propose three relaxations in simplified forms with a parameter λ: Lagrangian, completely positive, and copositive relaxations. These relaxations are obtained by reducing the QOP to an equivalent QOP with a single quadratic equality constraint in nonnegative va...

Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles’ carrying states within space–time transportation networks, so as to a...

We present numerical approximations of the 3D steady state Navier-Stokes equations in velocity-pressure formulation. We use trivariate splines of arbitrary degree d and arbitrary smoothness r < d. Using functional arguments, we derive the discrete Navier-Stokes equations in terms of B-coefficients of trivariate splines over a tetrahedral partition of any given polygonal domain. Smoothness condi...