Yuan’s theorem of the alternative is an important theoretical tool in optimization, which provides a checkable certificate for the infeasibility of a strict inequality system involving two homogeneous quadratic functions. In this paper, we provide a tractable extension of Yuan’s theorem of the alternative to the symmetric tensor setting. As an application, we establish that the optimal value of...

Many optimization problems gain from being interpreted and solved in either primal or dual form. For a user with a particular application, one of these forms is usually much more natural to use, but this is not always the most efficient one. This paper presents an implementation in the optimization modelling tool YALMIP that allows the user to define conic optimization problems in a preferred f...

We present alfonso, an open-source Matlab package for solving conic optimization problems over nonsymmetric convex cones. The implementation is based on the authors’ corrected analysis of a method Skajaa and Ye. It enables any cone as long logarithmically homogeneous self-concordant barrier available or its dual. This includes many cones, example, hyperbolicity cones their duals (such sum-of-sq...

This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating program for separating cuts, and investigate the impact of normalization condition its resolution. In particular, show that careful selection guarantees solvability strong duality. Then, highlight shortcomings conic-infeasible points an outer-approximation c...

Detecting infeasibility in conic optimization and providing certificates for infeasibility pose a bigger challenge than in the linear case due to the lack of strong duality. In this paper we generalize the approximate Farkas lemma of Todd and Ye [12] from the linear to the general conic setting, and use it to propose stopping criteria for interior point algorithms using self-dual embedding. The...

This research seeks to investigate the frequency and profitability of index arbitrage opportunities involving the SET50 futures, SET50 component stocks, and the ThaiDEX SET50 ETF (ticker symbol: TDEX). In particular, the frequency and profit of arbitrage are measured in the following three arbitrage tests: (1) SET50 futures vs. ThaiDEX SET50 ETF, (2) SET50 futures vs. SET50 component stocks, an...

This paper is devoted to studying the robust isolated calmness of the Karush– Kuhn–Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both t...