Related papers: The Complexity of the Homotopy Method, Equilibrium…
Let T be a general complex tensor of format $(n_1,...,n_d)$. When the fraction $\prod_in_i/[1+\sum_i(n_i-1)]$ is an integer, and a natural inequality (called balancedness) is satisfied, it is expected that T has finitely many minimal…
Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…
We find that imposing the crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When the crossing symmetry is not imposed, the convergence of…
In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration.…
In cooperative game theory, the primary focus is the equitable allocation of payoffs or costs among agents. However, in the practical applications of cooperative games, accurately representing games is challenging. In such cases, using an…
The sequence form, owing to its compact and holistic strategy representation, has demonstrated significant efficiency in computing normal-form perfect equilibria for two-player extensive-form games with perfect recall. Nevertheless, the…
Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A…
In this paper, we introduce a homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of two-person zero-sum discounted stochastic ARAT game. We show that the algorithm has the…
Poset games are a class of combinatorial game that remain unsolved. Soltys and Wilson proved that computing wining strategies is in \textbf{PSPACE} and aside from special cases such as Nim and N-Free games, \textbf{P} time algorithms for…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
Recent results in homotopy and solution paths demonstrate that certain well-designed greedy algorithms, with a range of values of the algorithmic parameter, can provide solution paths to a sequence of convex optimization problems. On the…
Given a C^1 path of systems of homogeneous polynomial equations f_t, t in [a,b] and an approximation x_a to a zero zeta_a of the initial system f_a, we show how to adaptively choose the step size for a Newton based homotopy method so that…
The equilibrium selection problem in the generalized Nash equilibrium problem (GNEP) has recently been studied as an optimization problem, defined over the set of all variational equilibria achievable through a lower-level non-cooperative…
This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed…
Homotopy methods are attractive due to their capability of solving difficult optimisation and optimal control problems. The underlying idea is to construct a homotopy, which may be considered as a continuous (zero) curve between the…
It is well-known that the winning region of a parity game with $n$ nodes and $k$ priorities can be computed as a $k$-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
Game theory finds nowadays a broad range of applications in engineering and machine learning. However, in a derivative-free, expensive black-box context, very few algorithmic solutions are available to find game equilibria. Here, we propose…
The paper aims to show the equivalency between nonlinear complementarity problem and the system of nonlinear equations. We propose a homotopy method with vector parameter $\lambda$ in finding the solution of nonlinear complementarity…
We show that the BIMATRIX game does not have a fully polynomial-time approximation scheme, unless PPAD is in P. In other words, no algorithm with time polynomial in n and 1/\epsilon can compute an \epsilon-approximate Nash equilibrium of an…